{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Table of Contents](./table_of_contents.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have developed the theory for the linear Kalman filter. Then, in the last two chapters we broached the topic of using Kalman filters for nonlinear problems. In this chapter we will learn the Extended Kalman filter (EKF). The EKF handles nonlinearity by linearizing the system at the point of the current estimate, and then the linear Kalman filter is used to filter this linearized system. It was one of the very first techniques used for nonlinear problems, and it remains the most common technique. \n",
    "\n",
    "The EKF provides significant mathematical challenges to the designer of the filter; this is the most challenging chapter of the book. I do everything I can to avoid the EKF in favor of other techniques that have been developed to filter nonlinear problems. However, the topic is unavoidable; all classic papers and a majority of current papers in the field use the EKF. Even if you do not use the EKF in your own work you will need to be familiar with the topic to be able to read the literature. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearizing the Kalman Filter\n",
    "\n",
    "The Kalman filter uses linear equations, so it does not work with nonlinear problems. Problems can be nonlinear in two ways. First, the process model might be nonlinear. An object falling through the atmosphere encounters drag which reduces its acceleration. The drag coefficient varies based on the velocity the object. The resulting behavior is nonlinear - it cannot be modeled with linear equations. Second, the measurements could be nonlinear. For example, a radar gives a range and bearing to a target. We use trigonometry, which is nonlinear, to compute the position of the target.\n",
    "\n",
    "For the linear filter we have these equations for the process and measurement models:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= \\mathbf{Ax} + w_x\\\\\n",
    "\\mathbf z &= \\mathbf{Hx} + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "Where $\\mathbf A$ is the systems dynamic matrix. Using the state space methods covered in the **Kalman Filter Math** chapter these equations can be transformed into \n",
    "$$\\begin{aligned}\\bar{\\mathbf x} &= \\mathbf{Fx} \\\\\n",
    "\\mathbf z &= \\mathbf{Hx}\n",
    "\\end{aligned}$$\n",
    "\n",
    "where $\\mathbf F$ is the *fundamental matrix*. The noise $w_x$ and $w_z$ terms are incorporated into the matrices $\\mathbf R$ and $\\mathbf Q$. This form of the equations allow us to compute the state at step $k$ given a measurement at step $k$ and the state estimate at step $k-1$. In earlier chapters I built your intuition and minimized the math by using problems describable with Newton's equations. We know how to design $\\mathbf F$ based on high school physics.\n",
    "\n",
    "\n",
    "For the nonlinear model the linear expression $\\mathbf{Fx} + \\mathbf{Bu}$ is replaced by a nonlinear function $f(\\mathbf x, \\mathbf u)$, and the linear expression $\\mathbf{Hx}$ is replaced by a nonlinear function $h(\\mathbf x)$:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= f(\\mathbf x, \\mathbf u) + w_x\\\\\n",
    "\\mathbf z &= h(\\mathbf x) + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "You might imagine that we could proceed by finding a new set of Kalman filter equations that optimally solve these equations. But if you remember the charts in the **Nonlinear Filtering** chapter you'll recall that passing a Gaussian through a nonlinear function results in a probability distribution that is no longer Gaussian. So this will not work.\n",
    "\n",
    "The EKF does not alter the Kalman filter's linear equations. Instead, it *linearizes* the nonlinear equations at the point of the current estimate, and uses this linearization in the linear Kalman filter. \n",
    "\n",
    "*Linearize* means what it sounds like. We find a line that most closely matches the curve at a defined point. The graph below linearizes the parabola $f(x)=x^2-2x$ at $x=1.5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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vZvmxY8fw3nvvFbiOj48P/vjjjzzL/v77bzRv3rzQHUyhUEChUORbPq6jGzYFP8PC44/gWsMeretavcW7oZeUSiUMDAxgaWnJP/pSxtyKh7kVD3MrHuZWXGZmZpqfhX0JSSXDfbf0ZOeo8VtwFIZ41YSO9P+vphH7MnpRhzmdOXMmNmzYgE2bNuHWrVuYMWMGoqKi8NFHHwHI/fZ/+PDhmvYfffQRHj58iJkzZ+LWrVvYtGkTNm7ciE8++aTYfU9sWwvvNXFAjlrAhG0huBObWmrvi4iIiIhITIIg4Iu9VzHn4A18+vuVMu1b1HsQBg0ahPj4ePzvf/9DdHQ0GjZsiMOHD6NmzZoAgOjo6DxzItSqVQuHDx/GjBkzsHLlSjg4OGDZsmV4//33i923RCLB4v6N8DQpA8EPEjFqczD2T2oJG2O9Unt/RERERERi+OWfCOy7/AQ6Ugnea1KtTPsW/SbliRMnYuLEiQW+5ufnl29Z27ZtERoaWip9K2Q6WOfbHP1WX8D9uDSM3XIJu8b5QF9Xp1S2T0RERERU2nZfeoRlxyMAAN/1aYi29azLtH9RLzEqD8wNdbF5ZAuYG8hx5XEypu26DJVatLnhiIiIiIhK7FxEHGbvuwYAmNS+NgZ71ijzGCp9gQAATlaGWD+8OXRlUvx9MxYLDt9680pERERERGXodkwKJmwLQY5awHtNHPBJFxetxFElCgQAaO5kgR8HNAYAbDh3H1sDHmg3ICIiIiKif8UkZ2LU5mCkZuXAq5YFFvdvpLVJf6tMgQAAvRs74NOuuZXY14du4MTtWC1HRERERERV3YusHIzyC0Z0ciZqWxtinW9zKGTau2e2ShUIADCxXW0Mau4ItQBM3nEZ158kazskIiIiIqqilCo1Jm0Pxa3oFFgZ6cJvlCdMDbQ7f0SVKxAkEgm+7dsQretYIT1bhQ+3BONJUoa2wyIiIiKiKkYQBMw9eB2n7zyHvlwHG0e0gKOFgbbDqnoFAgDIdaRYNawZXGyNEZuShRGbgpCUnq3tsIiIiIioCll1KhI7gx5BKgGWfdAUjR3NtB0SgCpaIACAiZ4cm0e1gJ2JHu4+e4Fxv4YgU6nSdlhEREREVAUcDHuCH46GAwC+7tUAnd1stRzR/6uyBQIAOJjpw290CxjryRD0IAEzd4dxjgQiIiIiElXgvXh8uucqAODD1rUwoqWTdgP6jypdIACAq50J1vk2h66OFIevxeCbP29CEFgkEBEREVHpuxObinFbQ5CtUqNbAzt82aO+tkPKp8oXCADgU9sSPw3MnSPB78IDrDtzT8sREREREVFlE52cgRGbgpCcoUSzGmZYMrgJpFLtzHXwOiwQ/tWrsQO+eje3gltw5DYOhj3RckREREREVFkkpysxYlOQZq6DjSNaQE+uvbkOXocFwivGtHHGh61rAQA+2XMF5+/GaTkiIiIiIqroMpUqjP31Eu7EvoCtiQJbRnvC3FBX22EVigXCf3zZoz7ebWQPpUrA+K0huPk0RdshEREREVEFpVILmLbrMoIeJMBYT4Ytoz1R3Vz7cx28DguE/5BKJfh5YGN4O1vgRVYORm4OwuPEdG2HRUREREQVzMuJ0I7eiIWujhTrhzeHq52JtsN6IxYIBVDIdLDWtzlcbI3xLDULIzcHcyI1IiIiIiqWFSfuYntgFCQSYMngJvB2ttR2SEXCAqEQpvpy+I1uAXvT3InUxmy5xInUiIiIiKhIdgVF4adjdwAA83o1QA93ey1HVHQsEF7D3lQffqM8Yawnw6WHiZiy8zJyVGpth0VERERE5dg/N2Mxe/81AMCk9rXL3URob8IC4Q1c7Iyxfnhz6MqkOPbvL5sTqRERERFRQUIeJmLyzlCoBWCAR3V80sVF2yEVGwuEIvB2tsTyD5pCKgF2X3qMhf63tR0SEREREZUzd5+9wIdbgpGpVKODqw0W9HOHRFL+JkJ7ExYIRdS1gR0W9msEAFh7+h7WnYnUckREREREVF7EJGdixKYgJKUr0cTRDCuGNIVMp2J+1K6YUWvJwBaO+KK7KwDg+8O3sefSIy1HRERERETalpiWDd+NgXiSlAFnK0NsGtkCBroybYdVYiwQiumjtrUx7h1nAMAX+67h2M1YLUdERERERNqSlpWDUX7BiHj2/7MkW5TjWZKLggVCCczq7or+HtWhUguYtCMUgffitR0SEREREZWxrBwVxm8NQdijJJgZyLHtQy84WpTvWZKLggVCCUgkEizs545O9W2RnaPGmC2XcONpsrbDIiIiIqIykqNSY9rOMJy7GwcDXR34jfJEXVtjbYdVKlgglJBMR4oVQ5rCs5YFUrNyMGJTMB7Gp2k7LCIiIiISmSAI+HL/dfjfiIGujhTrhzdHE0czbYdValggvAU9uQ42jGiO+vYmiHuRhWEbA/EsJVPbYRERERGRSARBwIIjt/HbpUeQSoBlHzRFqzpW2g6rVLFAeEsmenJsGd0CNS0N8CghA8M3BSE5Q6ntsIiIiIhIBKtPR2LdmXsAgIX9GqFbQzstR1T6WCCUAhtjPWwd7QVrYwVux6TiQ79gpGfnaDssIiIiIipFOwKjsNg/HADw1bv1MbCFo5YjEgcLhFJSw9IAv472hLGeDJceJmL81hBk5ai0HRYRERERlYI/rjzFlweuAQAmta+NMW2ctRyReEQtEBITE+Hr6wtTU1OYmprC19cXSUlJhbZXKpX4/PPP4e7uDkNDQzg4OGD48OF4+vSpmGGWmvr2JvAb5QkDXR2cjYjDlB2XoVSptR0WEREREb2F03eeY+buMAgCMNSrBj7p4qLtkEQlaoEwZMgQhIWFwd/fH/7+/ggLC4Ovr2+h7dPT0xEaGoo5c+YgNDQU+/btw507d9C7d28xwyxVHjXNsWF4c+jKpPj7Ziw+3XMFarWg7bCIiIiIqARCHibgo60hUKoE9Gxkj/+91xASiUTbYYlKtDmgb926BX9/f1y8eBFeXl4AgPXr18PHxwfh4eFwcclfeZmamuLYsWN5li1fvhyenp6IiopCjRo1xAq3VLWsY4XVQ5th/NYQHAh7CgOFDN/1qfw7ExEREVFlcv1JMkZtDkaGUoW29azx88Am0JFW/s9zop1BCAgIgKmpqaY4AABvb2+YmpriwoULRd5OcnIyJBIJzMzMRIhSPB3r2+KXQU0gleTe0PL94VsQBJ5JICIiIqoI7sSmYvimIKRk5qB5TXOsGeYBXVnVuH1XtDMIMTExsLGxybfcxsYGMTExRdpGZmYmvvjiCwwZMgQmJiYFtsnKykJWVpbmeUpKCoDc+xmUSu0ON9rNzRrfvtcAsw/cwPqz96Evk2JKh9pajeltvcyptnNbGTG34mFuxcPcioe5Fder+WWOS1dl2HcfxKdh6IZgJKRlw72aCdYNawqZRA2lUrv3lpZVTotdIMybNw/z589/bZvg4GAAKPCSGkEQinSpjVKpxODBg6FWq7Fq1apC2y1YsKDAeE6ePAkDA4M39iM2QwD9nCTY90AHy05GIureHbR3qPhnEv57KRiVHuZWPMyteJhb8TC34oiMjAQABAYGIi4uTsvRVE4Vdd9NyAKWXtdBUrYEDgYCPrBPwNkTf2s7LAC59+uWhWIXCJMnT8bgwYNf28bJyQlXr15FbGxsvteeP38OW1vb166vVCoxcOBA3L9/HydOnCj07AEAzJo1CzNnztQ8T0lJgaOjI9q3bw9LS8s3vJuy0QNAzVP38MvxuzjwUAcejd0wuEV1bYdVIkqlEseOHUPnzp0hl8u1HU6lwtyKh7kVD3MrHuZWXEFBQQAALy8veHp6ajmayqUi77sxKZkYsiEYSdkZcLYyxI4Pm8PSSKHtsDTi4+PLpJ9iFwhWVlawsnrzdNI+Pj5ITk5GUFCQ5g8vMDAQycnJaNmyZaHrvSwOIiIicPLkyTd+yFcoFFAo8v/i5HJ5udopp3aqh4wcAWtOR2LuHzdhrK+LPk2raTusEitv+a1MmFvxMLfiYW7Fw9yK42VOmV/xVLTcxr3Iwki/EDxKzEANCwPsGOsNO1M9bYeVR1nlU7Q7LerXr49u3bph7NixuHjxIi5evIixY8eiZ8+eeUYwcnV1xf79+wEAOTk56N+/Py5duoTt27dDpVIhJiYGMTExyM7OFivUMiGRSPB5NxcM96kJQQA+3nMFR28U7V4MIiIiIhJPUno2fDcGIfJ5GuxN9bB9jFe5Kw7Kkqi3Ym/fvh3u7u7o0qULunTpgkaNGmHr1q152oSHhyM5ORkA8PjxYxw6dAiPHz9GkyZNYG9vr3kUZ+Sj8koikWBerwZ4v1l1qNQCpuy4jNN3nms7LCIiIqIqKzVTiRGbgnArOgXWxgrsGOsNRwvt38eqTaKNYgQAFhYW2LZt22vbvDr0p5OTU6UfClQqlWDR++5Iz87BkesxGPfrJWwc0QKt6775si0iIiIiKj3p2TkY7ReMK4+TYW4gx/YxXqhlZajtsLSuagzmWs7IdKRYOrgpOtW3RVaOGmN+DUZAZNncdEJEREREQKZShXG/hiD4QSKM9WTY+qEX6tkaazuscoEFgpboyqRYObQp2rtYI1Opxmi/YATdT9B2WERERESVXnaOGpO2h+Lc3TgY6upgy2hPNKxmqu2wyg0WCFqkkOlg9TAPtKlrhQylCiM3ByHkIYsEIiIiIrEoVWpM2RmK47efQSGTYuPIFmhWw1zbYZUrLBC0TE+ug/XDm6NVHUukZ6swYlMwLkclajssIiIiokpHqVJjyo7LOHojFroyKdYNbw5v5/Ixb9abHD58GP/73//KpC8WCOWAnlwHG4a3gLezBV5k5WD4piBcfZyk7bCIiIiIKg2lSo2pOy/D/0YMdHWkWOfrgbb1rLUd1hvdvXsXPXv2xLvvvotly5aVSZ8sEMoJfV0dbBzRAi2czJGamYNhGwJx/UmytsMiIiIiqvByVGpM3xWGI9dzi4O1vh5o52Kj7bBe68WLF5g9ezYaNGiAv/76C3K5HJMmTSqTvlkglCOGChk2j/JEsxpmSMnMwbCNgbj5NEXbYRERERFVWDkqNab/Foa/rkVDriPBGt9maO9avouDQ4cOwdXVFQsWLEB2dja6du2Ka9euYf78+WXSPwuEcsZIIcOW0Z5o7GiGpHQlhm0MRHhMqrbDIiIiIqpwclRqzNh9BX9ezS0OVg/1QAdXW22H9UZJSUl48uQJnJ2dcfDgQRw5cgQuLi5l1j8LhHLIWE+OX0d7wr2aKRLSsjF0w0XcfcYigYiIiKioclRqzNx9BX9ceQq5jgSrhnqgk1v5LA4SEhIQFBSkeT5s2DCsX78eN27cQO/evSGRSMo0HhYI5ZSpvhxbP/SEm70J4l5kY/C6QETEskggIiIiehOVWsAne67g0JWnkEklWDmkGTqXw+JApVJh7dq1qFevHvr06YPU1NzPelKpFGPGjIGenp5W4mKBUI6ZGehi+xgv1Lc3QdyLLAxed5GXGxERERG9hkot4NM9V3AgLLc4WDGkGbo0sNN2WPlcuHABnp6e+OijjxAfHw9LS0s8ffpU22EBYIFQ7pkb6mLHGC80cDBBfFo2Bq8L4I3LRERERAVQqQV8+vsV7Lv8BDpSCVYMaYpuDctXcRAdHQ1fX1+0atUKoaGhMDMzw7Jly3D58uUyvc/gdVggVAC5RYI3GlU3RWK6EkM2XOQQqERERESvUKkFfPb7VewLzS0Oln/QFN0a2ms7rDxiYmLg4uKCbdu2QSKRYMyYMbhz5w6mTJkCmUym7fA0WCBUEKYGcmz90AtN/h3daMj6i7jyKEnbYRERERFpXe4NyWHYG/oYOlIJlg1uih7u5as4AAA7Ozv07NkT3t7eCAoKwvr162FtXf4ma2OBUIG8vHHZo6Z57jwJGwIRGpWo7bCIiIiItCY7R40pOy/j4Mt7Dj5oincblY/iIDIyEgMHDkRUVJRm2bp163D+/Hk0b95ci5G9HguECsZYT44toz3h6WSB1KwcDN8YhJCHCdoOi4iIiKjMZeWoMHF7iGaG5DXDPNC9HJw5SEtLw1dffYUGDRpgz549+OyzzzSvGRkZQSot3x/By3d0VCAjhQx+o1vA29kCL/4tEoLus0ggIiKiqiNTqcLYX0Pwz61nUMikWDdc+/McCIKA3bt3o379+vjuu++QlZWFzp074+uvv9ZqXMXFAqGCMtCVYfNIT7SqY4m0bBVGbApCQGS8tsMiIiIiEl16dg5G+wXjzJ3n0JfrYPPIFmjnYqPVmK5du4YOHTpg0KBBePToEZycnLB//34cPXoU9evX12psxcUCoQLT19XBxhEt0KauFTKUKozyC8L5u3HaDouIiIhINC+ycjByUzAuRMbDUFcHW0Z7omUdK22Hhd9++w2nTp2Cnp4e5s+fj5s3b6JPnz5lPgtyaWCBUMHpyXWwfnhztHOxRqZSjdF+wTh5+5m2wyIiIiIqdckZSvhuDETQgwQY68mwdYwXPGtZaCUWlUqF2NhYzfNZs2Zh/PjxuH37NubOnQt9fX2txFUaWCBUAnpyHaz19UCn+jbIylFj3NZLOHwtWtthEREREZWapPRsDNsQiMtRSTAzkGPHGG80q2GulVguXrwILy8v9OrVC2q1GgBgaGiINWvWoGbNmlqJqTSxQKgkFDIdrB7mgZ6N7KFUCZi8IxS/hzzWdlhEREREby3+RRYGr7uIa0+SYfnvBLLu1U3LPI6YmBiMHDkSPj4+CAkJQXh4OG7fvl3mcYiNBUIlIteRYungphjYvDrUAvDJniv4NeCBtsMiIiIiKrFnKZkYvO4ibsekwtpYgV3jvOHmYFKmMWRnZ+Onn35CvXr1sGXLFgDA6NGjERERATc3tzKNpSyUnzmdqVToSCVY2K8RDBUybD7/AHMP3sCLrBxMbFdH26ERERERFcujhHQM3RCIqIR02JnoYcdYLzhbG5VpDI8fP0bnzp01ZwpatGiBFStWwNPTs0zjKEs8g1AJSaUSzO3phqkdcouCxf7hWOx/G4IgaDkyIiIioqK5E5uK91dfQFRCOmpYGGDPRz5lXhwAgIODA4yMjGBtbY2NGzfi4sWLlbo4AFggVFoSiQQzu7hgVndXAMCqU5GY/8dNqNUsEoiIiKh8u/IoCQPXBuBZahZcbI3x+0c+cLQwKJO+09PTsWjRIqSlpQEApFIpdu7ciTt37mD06NHlfhbk0sBLjCq58W1rw1Ahw5yD1+F34QFeZOVg0fuNoCOteGPyEhERUeUXEBmPMVuCkZatQmNHM2wZ1QJmBrqi9ysIAvbu3YuPP/4YUVFRePHiBb755hsAQJ06VetSbRYIVcAw75owVOjgkz1X8XvIY2Rkq/DLoCbQlVX+CpiIiIgqjn9uxmLijlBk56jRsrYl1g1vDiOF+B9Xb9y4galTp+LEiRMAgBo1aqBZs2ai91te8RNiFdG3aXWsHNIMch0J/roWjfFbLyFTqdJ2WEREREQAgAOXn2D8thBk56jR2c0Wm0a2EL04SEpKwvTp09G4cWOcOHECCoUCc+fOxa1bt9C3b19R+y7PWCBUId0a2mHDiBbQk0txMvw5RmwKQkqmUtthERERURW3NeABZuwOg0otoF/Talg9tBn05Dqi9/vJJ59g6dKlUKlU6NOnD27duoX58+fDwKBs7ncor0QtEBITE+Hr6wtTU1OYmprC19cXSUlJRV5//PjxkEgkWLJkiWgxVjVt61nj19FeMFbIEHg/AYPWXsSz1Exth0VERERVkCAIWHnyLuYcvAFBAEb41MSPAxpDpiPeR1SV6v+voJg7dy6aNWuGo0ePYv/+/ahVq5Zo/VYkohYIQ4YMQVhYGPz9/eHv74+wsDD4+voWad0DBw4gMDAQDg4OYoZYJXnWssCu8d6wMlLgVnQK+q8OwMP4NG2HRURERFWIIAhY6H8bPxwNBwBM6VAH83o3gFSkgVRiY2MxatQojBw5UrOsRo0auHTpErp06SJKnxWVaAXCrVu34O/vjw0bNsDHxwc+Pj5Yv349/vzzT4SHh7923SdPnmDy5MnYvn075HK5WCFWaQ0cTLF3gg9qWhogKiEd768OwPUnydoOi4iIiKqAHJUas/dfw9rT9wAAX/aoj4+7uEAiKf3iQKlU4pdffkG9evXg5+eH7du3IyIiQvO6GH1WdKIVCAEBATA1NYWXl5dmmbe3N0xNTXHhwoVC11Or1fD19cWnn36KBg0aiBUeAahpaYg9H/nAzd4EcS+yMHjdRQRExms7LCIiIqrEMpUqTNgeip1BjyCRAAv7uWPsO86i9PXPP/+gcePGmDlzJlJSUuDh4YHz58+jbt26ovRXWYh2a3hMTAxsbGzyLbexsUFMTEyh6y1atAgymQxTp04tUj9ZWVnIysrSPE9JSQGQWy0qlbwB903M9XSwbbQHJuwIQ+D9RAzfFIhfBjRC1wa2BbZ/mVPmtvQxt+JhbsXD3IqHuRXXq/lljkvX6/bdpHQlxm+/jNCoJOjKpPi5vzu6NrAt9d9BbGwspkyZggMHDgAArKys8O2332LkyJGQSqUV9ndeVnEXu0CYN28e5s+f/9o2wcHBAAo+ZSMIQqGnckJCQrB06VKEhoYW+XTPggULCozn5MmTVf4O9OIYYANkJEtxNUGKKbvCMNBZjZa2hc+6fOzYsTKMrmphbsXD3IqHuRUPcyuOyMhIAEBgYCDi4uK0HE3l9N99NzELWHNLBzEZEujrCBjrkg3VwxAcflj6fWdkZOD06dOQSqXo3r07PvjgAxgZGcHf37/0OytD6enpZdKPRBCEwj8FFiAuLu6Nf0hOTk7YsWMHZs6cmW/UIjMzM/zyyy8YNWpUvvWWLFmCmTNn5pnCWqVSQSqVwtHREQ8ePMi3TkFnEBwdHREdHQ1LS8vivLUqT6UW8PUfN/HbpScAgBkd62BC21p5ijWlUoljx46hc+fOvD+klDG34mFuxcPcioe5FVdQUBBat26Nc+fOwdPTU9vhVCoF7bsRsS8w6tcQxKZkwdZEgU3Dm6GerXGp9SkIAk6cOIH27dtrPkf+888/sLW1hbu7e6n1o23x8fGwt7dHcnIyTExMROun2GcQrKysYGVl9cZ2Pj4+SE5ORlBQkOYPLzAwEMnJyWjZsmWB6/j6+qJTp055lnXt2hW+vr4FFhQAoFAooFAo8i2Xy+U8oBaTHMDC9xvD2lgfK07exS/H7yIxIwdze7rlG1GA+RUPcyse5lY8zK14mFtxvMwp8yuel7kNfpCAD/2CkZKZgzo2Rtgy2hPVzPRLrZ+bN29i2rRp+Oeff/Drr79qRszs3r17qfVRXpTVviraPQj169dHt27dMHbsWKxduxYAMG7cOPTs2RMuLi6adq6urliwYAH69u0LS0vLfN/6y+Vy2NnZ5VmHxCORSPBJVxdYGuli/h834XfhAeLTsvHjgEZQyMSfsISIiIgqj6M3YjB152Vk5ajRrIYZNo1sATMD3VLZdnJyMubPn4/ly5cjJycHCoUCz58/L5VtV3WizoOwfft2uLu7o0uXLujSpQsaNWqErVu35mkTHh6O5GQOr1nejGpVC0sHN4FMKsEfV55i5KZgJGdUzBt6iIiIqOztCn6MCdtCkJWjRqf6Ntg+xrtUigO1Wo3NmzejXr16+OWXX5CTk4P33nsPN2/exMyZM0shchLtDAIAWFhYYNu2ba9t86ZbIAq674DKxntNqsHCUBcTtoUi4F48Bqy5gPXDmmo7LCIiIirHBEHAkUcS+AfcBAAMau6I7/o2LLXZkcePH48NGzYAAOrVq4elS5eiW7dupbJtyiXqGQSq+NrUtcZv471ha6LAndgXGLAuCI856TIREREVIEelxtw/bsH/ce5lyVM71MHC991LrTgAgJEjR8LY2Bg//PADrl27xuJABKKeQaDKoYGDKfZPbIVRm4MRHpuKZdd1UL9JHDq42Ws7NCIiIion0rJyMGXnZZy4/QwSCPi6lxtGtnq7CdCUSiVWrVqFnJwcfPzxxwCAVq1a4dGjRzA1NS2NsKkAPINAReJgpo/dH/nAx9kCWWoJxm67jN3Bj7QdFhEREZUDsSmZGLg2ACduP4NCJsWoemoM9XR8q22ePHkSTZs2xfTp0/HVV18hKipK8xqLA3GxQKAiM9WXY4NvM7SwUkOlFvDZ3qv4+didN95HQkRERJXX7ZgU9Fl5HjeepsDSUBfbRjdHY8uSfzaIiorCwIED0aFDB9y4cQOWlpZYunQpqlWrVopR0+uwQKBi0ZVJMbSOGhPb5p4yXHY8Ap/suYrsHLWWIyMiIqKydubOc/RfHYDo5Ew4Wxti/8RWaOJoVqJtZWZm4ptvvoGrqyv27NkDqVSKSZMm4c6dOxg3bhx0dDjcellhgUDFJpEAMzrVwYJ+7tCRSrA39DFG+wUjNZPDoBIREVUVu4KiMMovGC+ycuBVywL7JrREDUuDEm8vOjoa3333HTIyMvDOO+/g8uXLWLFiBSwsLEoxaioKFghUYh941sCGEc1hoKuDc3fjMGBNAKKTM7QdFhEREYlIrRaw2P82vth3DSq1gL5Nq+HXDz1LNMdBbGys5t+1atXCokWLsHPnTpw6dQqNGjUqzbCpGFgg0Ftp72KD3eN9YG2swO2YVPRZeR7XHnPiOyIiosooU6nCtN/CsOpUJABgase6+HlgYyhkxbv8JyUlBZ9++ilq1KiBixcvapZPmzYNgwcPhkQiKdW4qXhYINBba1jNFPsntkQ9WyPEpmRhwNoL8L8ere2wiIiIqBQlpmXDd2Mg/rjyFDKpBD/0b4SZnesV68O8Wq3Gr7/+ChcXF/z444/Izs7G/v37RYyaSoIFApWK6uYG2DuhJdq5WCNTqcZH20Kx8uRdjnBERERUCTyIS0O/1RcQ/CARxnoybBntiQHNizeMaWhoKFq3bo0RI0YgJiYGdevWxV9//YVFixaJFDWVFAsEKjXGenJsGN4cI1s6AQB+OBqOj/dcQVaOSruBERERUYldiIxDn1XncT8uDdXM9LF3Qku0qmNVrG18+eWXaN68OQICAmBoaIiFCxfi2rVr6NGjh0hR09tggUClSqYjxbzeDfBNn4bQkUqwL/QJhq4PRPyLLG2HRkRERMW0PfAhhm8MQlK6Eo0dzbB/UkvUszUu9nbq1KkDQRAwdOhQ3LlzB59//jkUCoUIEVNpkGk7AKqcfL1rwsnSABO3h+LSw0T0WXUeG0e0KNFBhYiIiMpWjkqNb/68iS0BDwEA7zVxwKL3G0FPXrSbka9fvw4dHR307NkTADBixAi4u7ujefPmosVMpYdnEEg0bepaY//EVqhpaYBHCRl4f9UFnAp/pu2wiIiI6DWS05UYuTlYUxx82tUFSwY1KVJx8PjxYwwbNgxfffUVPvroI7x48QIAIJVKWRxUICwQSFR1bIxwYGIreNayQGpWDkb7BWPLhQfaDouIiIgKEPn8BfqsOo9zd+NgoKuDNcM8MKl9nTeOVJSZmYnvv/8eLi4u2L17N6RSKXr27AmVivchVkS8xIhEZ26oi20feuHL/dewJ+Qxvj50A3efvcDcXm6Q67BGJSIiKg/ORjzHpO2hSMnMgYOpHjaMaAE3B5PXriMIAv78809Mnz4d9+7dAwC0atUK77//PiZPngy5XF4WoVMp46czKhO6MikW92+EL7q7QiIBtl58iGEbePMyERGRtgmCgC0XHmDk5mCkZObAo6Y5Dk5u/cbiAACuXLmC3r174969e3BwcMD27dtx4sQJODs7l0HkJBaeQaAyI5FI8FHb2nC2MsSM38IQeD8BvVecx1pfDzSsZqrt8IiIiKocpUqNrw/dwI7AKABAv2bVsKCf+2tnRlar1ZBKc79jbtKkCXx9fVGtWjV8+eWXMDIyglKpLJPYSTw8g0BlrksDOxyY1Aq1rAzxJCkD/ddcwMGwJ9oOi4iIqEpJSMvG8I1B2BEYBYkEmN3DFT8NaFxocSAIArZv3w5XV1c8fvxYs3zLli1YsGABjIyMyip0EhkLBNKKurbGODCplWbm5Wm7wrDg8C2o1Jx5mYiISGzXnySj1/JzCLgXD0NdHWwY3hzj3qld6M3Ily9fRps2bTBs2DBERETgxx9/1Lz2phuYqeJhgUBaY6ovx8YRLTChXW0AwNoz9zBycxCS0rO1HBkREVHltTfkMd5ffQFPkjJQy8oQ+ye1Qsf6tgW2jY+Px4QJE+Dh4YHz58/DwMAA33//PRYtWlTGUVNZYoFAWqUjleDzbq5YMaQp9OU6OBsRh/dWnkd4TKq2QyMiIqpUlCo1vj54HR/vuYKsHDU6utrgwKRWhU5iun79etStWxdr1qyBIAgYPHgwwsPDMWvWLM6CXMmxQKByoWcjB+yd0BLVzfXxMD4dfVedh//1GG2HRUREVCk8S83E0PWBmsnPpnWsi/XDm8NUv/BhSCMjI5GYmAh3d3ecOnUKO3fuRPXq1csqZNIiFghUbrg5mODQ5NZoWdsS6dkqfLQtBD8fuwM170sgIiIqsdCoRPRafg5BDxJgrJBh/fDmmNG5HqTSvPcOPHnyBLdv39Y8/+qrr7B27VqEhoaibdu2ZR02aRELBCpXLAx18etoT4xuVQsAsOx4BD7cEsz7EoiIiEpgZ1AUBq+9iNiULNSxMcKBya3Q2S3v/QZZWVlYuHAhXFxcMGrUKKjVagCAkZERxo0bB5mMo+JXNSwQqNyR6Ugxt5fbv0OtSXEy/Dl6Lj+Ha4+TtR0aERFRhZCVo8Ksfdcwa981ZKvU6PbvEOO1rfMORfrXX3+hYcOGmDVrFtLS0iCRSJCQkKClqKm8YIFA5db7HtWxd0JL1LAwwOPEDLy/+gJ2BEZBEHjJERERUWFikjMxeN1F7AzKnd/g064uWD2sGYwU/38mICIiAj179kTPnj1x9+5d2NnZ4ddff8X58+dhZWWlxeipPGCBQOVaw2qm+GNKa3Sqb4tslRqz91/DJ3uuIiNbpe3QiIiIyp2zEc/RY9lZXI5Kgqm+HJtHtsCk9nXyzFUQFBSEhg0b4q+//oJcLsenn36KO3fuwNfXl3MaEACAF5VRuWeqL8c6Xw+sPXMPPxy9jb2hj3HjaTJWD/NALStDbYdHRESkdSq1gGXHI7DsRAQEAXCzN8HqYc1Q0zL//5MeHh5o2LAhrK2tsXTpUri4uGghYirPeAaBKgSpVIIJ7Wpj2xgvWBnp4nZMKnovP8ehUImIqMqLe5GFEZuCsPR4bnHwgWcN7JvYUlMcXLlyBR988AHS09MBADo6Ojh+/DiOHDnC4oAKxAKBKpSWta3w19Q2aF7THKlZOfhoWwi+P3wLOSq1tkMjIiIqc0H3E9Bj6VmcuxsHfbkOfhnUGAv6uUNProOEhARMmjQJzZo1w65du/DDDz9o1jMzM+PlRFQoUQuExMRE+Pr6wtTUFKampvD19UVSUtIb17t16xZ69+4NU1NTGBsbw9vbG1FRUWKGShWIrYkedo7zxpjWuUOhrjtzD0M2BOJZSqaWIyMiIiobarWANacj8cH6i3iWmjuE6aHJrdC3aXWoVCqsWbMGdevWxapVq6BWqzFw4ECMGjVK22FTBSFqgTBkyBCEhYXB398f/v7+CAsLg6+v72vXiYyMROvWreHq6opTp07hypUrmDNnDvT09MQMlSoYuY4UX/V0w6qhuaMyBN1PQI9l53AuIk7boREREYkqKT0bY3+9hIVHbkOlFtCniQMOTmqFurbGOHfuHJo3b44JEyYgISEBDRs2xIkTJ/Dbb7+hRo0a2g6dKgjRblK+desW/P39cfHiRXh5eQEA1q9fDx8fH4SHhxd6zduXX36JHj16YPHixZplzs7OYoVJFVwPd3u42hljwrZQhMemwndTICa0rY2ZnetBpsMr6IiIqHIJe5SESdtD8SQpA7oyKeb1aoAPPB01lwv98ssvCAsLg5mZGf73v/9hwoQJnOiMik20PSYgIACmpqaa4gAAvL29YWpqigsXLhRYIKjVavz111/47LPP0LVrV1y+fBm1atXCrFmz0KdPnwL7ycrKQlZWluZ5SkoKAECpVEKpVJbumyJNTstTbh3NFPh9vCe+OxKOXcGPsepUJC7ei8cvA9zhYKav7fCKrDzmtrJgbsXD3IqHuRXXq/mtCDkWBAFbAx9hoX84lCoBNSz0sWxQY9SxVCAuLg5mZmYAgIULF8LS0hLz5s2DtbU1BEEo8/fHfVc8ZZVTiSDSrFPff/89/Pz8cOfOnTzL69Wrh1GjRmHWrFn51omJiYG9vT0MDAzw7bffon379vD398fs2bNx8uRJtG3bNt868+bNw/z58/Mt37FjBwwMDErvDVGFcDlegl2RUmSqJNDXEfBBbTUaW3JiNSIiyisyMhIff/wxfvrpJ9SuXVvb4bzWCyWwM1KK64m5Z8YbW6jxQW01bl4JwcaNG1GvXj1Mnz5du0FSmUhPT8eQIUOQnJwMExMT0fop9hmEwj6Qvyo4OBgACrw7XhCEQu+aV6tzR6J57733MGPGDABAkyZNcOHCBaxZs6bAAmHWrFmYOXOm5nlKSgocHR3Rvn17WFpaFu1NUZEplUocO3YMnTt3hlwu13Y4+fQAMDwxHdN3X8XVxynYdEcHw7wc8UXXelDIdbQd3muV99xWZMyteJhb8TC34goKCgIAeHl5wdPTU8vRFO7ivQR8//s1xKZmQa4jwedd66GVtRKffvop/vrrLwC5n598fHxgbm6u5Whzcd8VT3x8fJn0U+wCYfLkyRg8ePBr2zg5OeHq1auIjY3N99rz589ha2tb4HpWVlaQyWRwc3PLs7x+/fo4d+5cgesoFAooFIp8y+VyOXdKEZXn/DrbmOL3j1rhp7/DsfbMPWwLfISQqGSsGNIUta2NtB3eG5Xn3FZ0zK14mFvxMLfieJnT8ppfpUqNJf/cwapTkRAEwNnaEIveq4cDm1di0o8/Ijs7GzKZDNOmTcOcOXNgamqq7ZDzKa+5rcjKKp/FLhCsrKxgZWX1xnY+Pj5ITk5GUFCQpjIPDAxEcnIyWrZsWeA6urq6aNGiBcLDw/Msv3PnDmrWrFncUKkK05VJMatHffjUtsTHu6/gVnQKei0/h/+91xD9PaprOzwiIqJCPUpIx5SdlxH2KAkAMLiFI3o7ZqFfey88fvwYANC5c2csXboU9evX12KkVFmJNsxL/fr10a1bN4wdOxYXL17ExYsXMXbsWPTs2TPPDcqurq7Yv3+/5vmnn36K3377DevXr8fdu3exYsUK/PHHH5g4caJYoVIl1s7FBoentUHL2pZIz1bhkz1XMPO3MLzIytF2aERERPkcDHuCHkvPIuxREoz1ZFg5pBkWvt8IDV1doFQq4eTkhP379+Po0aMsDkg0oo4DuX37dri7u6NLly7o0qULGjVqhK1bt+ZpEx4ejuTkZM3zvn37Ys2aNVi8eDHc3d2xYcMG7N27F61btxYzVKrEbE30sPVDL3zSpR6kEmDf5dyDb8jDBG2HRkREBABIy8rBJ3uuYNquMKRm5cDdSgd9ZZfRw90OAGBiYgJ/f3/cvHkTffr04SzIJCpRB8a1sLDAtm3bXtumoEGURo8ejdGjR4sVFlVBOlIJJneoCy9nS0zfFYaohHQMWBOASe3rYGrHupBzzgQiItKSa4+TMXXXZdyPS4NEUKF51hWcXLgUf8bHw9W5BoYMGQIgd+AWorLAT0VUpbRwssCR6W3Qr2k1qAVg+Ym7eH/1BUQ+f6Ht0IiIqIpRqQWsOR2JfqvP435cGoyS70Hv8Fz8vnQu4uPj4ebmhurVed8clT0WCFTlmOjJ8fOgJlgxpClM9eW4+jgZ7y47i60XHxZ4RouIiKi0PYxPw6C1AVh45DYykxOge241bqyZitvXr8DExEQzI/I777yj7VCpCmKBQFVWz0YOODr9HbSuY4VMpRpzDlzHh1su4VlqprZDIyKiSkoQBOwIjEL3pWdx6WEijBQyGJ1fhojzuXMajB49GhEREZg+fTqHCCWtYYFAVZqdqR5+He2JuT3doCuT4sTtZ+i25Cz+vhGj7dCIiKiSeZaSidF+wZi9/xrSspTwrGWBI9PaYM2SH+Dl5YXAwEBs3LgRNjY22g6VqjhRb1ImqgikUglGt66FVnWsMP23MNyKTsG4rSEY3MIRc3q6wVDBPxMiIno7f12NxpcHruH500dIPrkRndp4Y9eCnyCVSuDYti0CAgI4MhGVGzyDQPQvFztjHJjUEuPfcYZEAuwKfoTuS8/i4r2ymdaciIgqn+R0JabvuowJWy7gwdHNiNk4EWl3AnByz0akpf3/ABksDqg8YYFA9AqFTAezetTHzrHeqGamj6iEdAxedxFfH7yONE6uRkRExXA24jm6/HIa23ftxtMNE5B8YRfUOdno2LEjAgICYGxsrO0QiQrEAoGoAN7OlvCf3gYfeNYAAGwJeIhuS88gIJJnE4iI6PXSsnIw9+B1DP7xAK6u/xhxBxdClfIcNWrUwO+//45jx47Bzc1N22ESFYoFAlEhjPXkWNDPHVs/9EQ1M308SsjAB+svYi7PJhARUSFyzxqcwa8BDwEAyie3oKenh6+//hq3bt3C+++/z8uJqNzj3ZdEb9CmrjX8p7fB94dvY2dQFH4NeIiT4c+w6P1GaFnbStvhERFROZCcocS3f1zH1oN/Q8+xIaqZ6WPhh33wpL0xvL294eTkpO0QiYqMBQJREbw8m/Cuuz0+33sVjxIyMGR9IHy9a+KL7q4c6YiIqAr7+0YMpi/fg8hDy5EdHYExP+zEkildc/9vqDtY2+ERFRsvMSIqhtZ1rXB0xjsY6pV7b8LWiw/RdckZXLgbp+XIiIiorMW/yMKHa/5Bv8G+uLV2KrKjI2BoZIROjhJ+cUQVGgsEomIyUsjwXV93bB/jhWpm+nicmIEhGwLxxd6rSE5Xajs8IiISmSAI2HfpIRoPmIbN095D2vV/AAC+w0fgbkQEBg0apOUIid4OCwSiEmpVJ+/ZhF3Bj9Dx51M4dOUpBEHQcnRERCSG2JRMjNlyCUP69cQT/7UQstPRoFFTBAQE4NctfrCzs9N2iERvjQUC0Vt4eTZh93gf1LExQtyLbEzdeRkjNwfjUUK6tsMjIqJSolYL2BEYhU4/n8bx289g4t4BRmYWWLN2Ha5evgRvb29th0hUalggEJUCz1oW+Gtqa8zoVA+6OlKcvvMcnX85jbWnI5GjUms7PCIieguhkbFo0GsMpi9ai9TMHDSuborT6/+HR/cjMX7cWEil/DhFlQv3aKJSopDpYFqnujgyvQ28alkgU6nGgiO30XvFeVx5lKTt8IiIqJheZCox5Mul8PJohNuHNyHp+HrM6uKMvRNaor6DKczMzLQdIpEoWCAQlbLa1kbYNc4bi99vBFN9OW5Gp6DvqvOYd+gGXnCCNSKiCmHdodOo7u6Nnd9PR07yMxhZ2mLlsl8wrr0rZDr8+ESVG/dwIhFIJBIMbOGI4x+3RZ8mDlALgN+FB+j882kcvRHDm5iJiMqpmw+j0bDbUIzv2xHJd0MhkcnhO2EmYqPuYeyIoZwFmaoEFghEIrIyUmDJ4Kb4dbQnHC30EZ2cifFbQzByczDux6VpOzwiIvqXUqXG2tOR6PblFtw4ugNQq+Dm0xHXr93Ar6t+goGBgbZDJCozLBCIysA79azx9/S2mNiuNuQ6Epy+8xxdfzmDxf63kZ7Ny46IiLTpn9AI9Fp+DguO3Ia0ujvqdRqC9Tv24saFf+DmWlfb4RGVORYIRGVEX1cHn3VzxdHp76BtPWtkq9RYdSoSHX86jb+uRvOyIyIiLRg84TN08WmC6xEPYG4gx+L+jXD7720Y80E/bYdGpDWcB5yojDlbG8FvVAscuxmL//15E48TMzBpRyh8nC3Qzljb0RERVX6p6Zn44oe1AID7oacBAG45Edj18WBYGOpqMzSicoFnEIi0QCKRoEsDO/wzsy2md6oLhUyKgHsJWHRVBwuOhCM1U6ntEImIKh1BELB40++wc66Pk79vAgAY2TjCb98R/L32GxYHRP9igUCkRXpyHUzvVA//zGyLTq7WUAsSbLrwEB1+Oo19oY+hVvOyIyKi0hARmwJnn274/MMBSI99AB09QwDA0f27MKJvNy1HR1S+sEAgKgccLQywemhTjHdVwcnSAM9TszBz9xX0XX0Blx4kaDs8IqIKKzlDif/9cRPdl55DgmAESKTw6TUE+3//HQAgk/Fqa6L/YoFAVI64mQv4c3JLfNrVBYa6OrjyKAn91wRgwrYQPIznsKhEREWVo1Lj4x/Ww/uTjdh0/j5y1ALeGzUFR05dwIVD22FrbaHtEInKLZbNROWMQibFpPZ1MKB5dfxy7A5+C36EI9dj8M+tWIzwccKUDnVhaiDXdphEROWSIAjY6n8BM2fMQHx4MBTV3NBqxkp83asB3qlnre3wiCoEnkEgKqdsjPWwoF8jHJ7WBu/Us4ZSJWDDufto++NJbDp3H9k5am2HSERUrly8/Qhu3YZiRM+2iA8PhkRHjo4d2uHQRG8WB0TFwAKBqJxztTPBr6M94TeqBerZGiEpXYn//XkTXX45jaM3Yjh/AhFVeVHxL9B14jdo3bwxbv+9E1Cr4OLZDpcuh+GvX1fCUF9P2yESVSiiFgiJiYnw9fWFqakpTE1N4evri6SkpNeu8+LFC0yePBnVq1eHvr4+6tevj9WrV4sZJlGF0M7FBoentsH3fd1hZaSLB/HpGL81BIPWXcSVR0naDo+IqMwlpyvx/eFb8BrzHf5ePReqtESY2dWA3669uB14Es3c3bQdIlGFJOo9CEOGDMHjx4/h7+8PABg3bhx8fX3xxx9/FLrOjBkzcPLkSWzbtg1OTk74+++/MXHiRDg4OOC9994TM1yick+mI8UQrxro3cQBa05FYv3Zewi6n4D3Vp5HtwZ2+LhLPdS15WxrRFS5ZSpV+PXCA6w8FYnkDCV06/rAuk5jDB3QFwu//gIKhULbIRJVaKKdQbh16xb8/f2xYcMG+Pj4wMfHB+vXr8eff/6J8PDwQtcLCAjAiBEj0K5dOzg5OWHcuHFo3LgxLl26JFaoRBWOkUKGT7q64OQn7dCvWTVIJID/jRh0WXIGM3eH4VFCurZDJCIqdSq1gD1BD+D2/nRMGdQViSkv4GpnjC0feiMmPBS/fP81iwOiUiDaGYSAgACYmprCy8tLs8zb2xumpqa4cOECXFxcClyvdevWOHToEEaPHg0HBwecOnUKd+7cwdKlSwtsn5WVhaysLM3zlJQUAIBSqYRSydloS9vLnDK3pa8kubU2lGFR3wYY07Imlpy4i79vPsO+0Cf448pTDPSojontnGFjzP8sud+Kh7kVD3P7/9RqAf43YjFv/V7c+H0JlHEPAQCdpDewasLn0JFKoFKpoFKpirzNV/PLHJcu7rviKaucilYgxMTEwMbGJt9yGxsbxMTEFLresmXLMHbsWFSvXh0ymQxSqRQbNmxA69atC2y/YMECzJ8/P9/ykydPwsDAoORvgF7r2LFj2g6h0ippbt81BRq6A4ejpLidLMX2oEfYfSkK79gJ6OighiFHRuV+KyLmVjxVObeCAFxLlODA9XjcPrwZ6bfPAgAUhsbwHToU3X0a4Kj/kRJtOzIyEgAQGBiIuLi4UouZ/l9V3nfFkp5eNlcIFLtAmDdvXoEfyF8VHBwMAJBIJPleEwShwOUvLVu2DBcvXsShQ4dQs2ZNnDlzBhMnToS9vT06deqUr/2sWbMwc+ZMzfOUlBQ4Ojqiffv2sLS0LOrboiJSKpU4duwYOnfuDLmcnzhLU2nldgKAwPsJ+OlYBC4/SsbxpxIExutiTGsnjPCpASNF1Zv+hPuteJhb8VTl3AqCgNMRcVhyLALn921ASsAeCDlZkEilGDV6DL77Zv5b/x8fFBQEAPDy8oKnp2dphE3/qsr7rtji4+PLpJ9if1KYPHkyBg8e/No2Tk5OuHr1KmJjY/O99vz5c9ja2ha4XkZGBmbPno39+/fj3XffBQA0atQIYWFh+PHHHwssEBQKRYHXG8rlcu6UImJ+xVMauW1dzxat6trgxO1n+OFoOG7HpGLJ8bv49WIUxrZxhq9PzSpZKHC/FQ9zK56qlFtBEHD+bjx+PhaO0KgkAIAq9i6EnCz4tGqNVSuWo0mTJqXS18ucVqX8ljXmtvSVVT6L/QnBysoKVlZWb2zn4+OD5ORkBAUFaSrzwMBAJCcno2XLlgWu8/I6QKk0773TOjo6UKs5KRRRcUgkEnSsb4v2Ljb481o0fv47HA/i07HI/zbWnonE6Fa1MKKlE0z1efAmIu0Lup+An/4Ox7mQa5AqDGBoZonhPk7oMmQj7lwPwwcffPDaKxCIqPSI9hVi/fr10a1bN4wdOxZr164FkDvMac+ePfPcoOzq6ooFCxagb9++MDExQdu2bfHpp59CX18fNWvWxOnTp/Hrr7/i559/FitUokpNKpWgd2MH9Ghoh4NhT7Hy5F3ci0vDz8fuYP2ZexjZygmjW9WCuaGutkMloipGEARciIzH8hMRuHDrMZIDfkNK8EE0adcTRw/shI1x7gRnzRtxPgOisiTqNQbbt2/H1KlT0aVLFwBA7969sWLFijxtwsPDkZycrHm+a9cuzJo1C0OHDkVCQgJq1qyJ7777Dh999JGYoRJVejIdKd73qI4+Tavhr2vRWHEiAndiX2D5ibvYdO4+hvnUxNg2zrAy4qhHRCQuQRBw4vYzLD9xF5ejEpF28xSSTm2G6kUCAKC6QQ4s9KveZZBE5YWof30WFhbYtm3ba9sIgpDnuZ2dHTZv3ixmWERVms6/ZxR6utvj6I0YLD9xFzejU7D29D1sufAAQ71qYvw7zrAx0dN2qERUyajUAvyvx2DFybu4FZ2C7NhIJP6zFpmPbwIA6tSpgyVLlmjuQyQi7WB5TlRFSaUSdHe3R7eGdjh+6xmWn4jAlcfJ2HjuPrZefIgBHtUxto0znKwMtR0qEVVwWTkqHLj8BOvO3EPk8zQAgOruBcTsWwBBEGBgYICvvvoKM2fO5ERnROUACwSiKk4ikaCTmy061rfBmYg4LD8egUsPE7E9MAo7gqLQvaEdxr1TG00czbQdKhFVMMkZSmwPfIjN5x/geWrupKYmejKMalUL/aa2gOfZDejYsSMWL16M6tWrazlaInqJBQIRAcgtFNrWs8Y7da0QeD8B687cw4nbz3D4WgwOX4uBZy0LfNTWGe3q2UAq5UgiRFS4p0kZ2HTuPnYGRSEtO3d2Y8OECFg/u4RDOzfBRD93UISbN29yziKicogFAhHlIZFI4O1sCW9nS4THpGLdmXs4dOUJgu4nIOh+AuraGGFsG2f0buIAPbmOtsMlonLk+pNkbDp3H4euPEWOOvcew5qKTKgDt+Lc0YMAAP8/emPgwIEAwOKAqJxigUBEhXKxM8ZPAxvjk671sPn8A+wIjELEsxf4bO9VLPS/jaFeNTDMuyZseUMzUZWlUgs4djMGm849QNCDBM3yFo5GMLt3DDtXLEFaWhokEgnGjRuHDh06aDFaIioKFghE9Eb2pvqY3aM+Jneog11BUdhy4SGeJGVg+Ym7WHM6Eu+622NUq1pozPsUiKqM5Awldgc/gt+FB3iSlAEAkEkl6OFuj7pZd7Dsu+m4e/cuAKBVq1ZYvnw5mjZtqs2QiaiIWCAQUZGZ6Mkx7p3aGN2qFo7djMWm8/cR/CARB8Ke4kDYU3jUNMeIlk7o1sAOujLpmzdIRBVORGwqtl58iN9DHiP93/sLzA3kGOJVA77eTrA2kqNxY1/cvXsX9vb2WLx4MYYOHcpZkIkqEBYIRFRsMh0purvbo7u7Pa49Tsbm8/fxx9WnCHmYiJCHibAy0sWgFo74wLMGqpsbaDtcInpL2Tlq/H0zBlsDHiLw/v9fRuRia4xRrZzQqa4pjA30NEOULl++HP7+/vjqq69gbGysrbCJqIRYIBDRW3GvboqfBzXBF91dsT0wCruCoxCbkoWVJyOx+lQkOrjaYJh3TbxT15qjHxFVME+TMrAzKAo7gx4h7kXuMKVSCdDZzRbDfZzg42yBXbt2oXHfTzFlyhR88cUXAID27dujffv22gydiN4CCwQiKhU2JnqY0bkeJneog39uxmJb4EOcvxuPf249wz+3nqGGhQEGezqif7PqnKWZqBzLUalx+s5z7Ax6hBO3Y/HvYESwNlbgA88a+MDTEfam+rhy5QrateuHs2fPAgB27tyJTz/9FDo6HN2MqKJjgUBEpUr+yuVHkc9fYPvFKOwJeYSohHQs9g/HT3/fQXsXGwxq4Yj2LtaQ6fBeBaLy4EFcGnZfeoTfQx7j2b+TmgGAj7MlfH1qorObLeQ6UsTHx2PixI+xdu1aqNVqGBgYYPbs2fj4449ZHBBVEiwQiEg0ta2NMLeXGz7t6oI/rj7F7uBHuPQwEf/cisU/t2JhY6zA+x7VMai5I5ysDLUdLlGVk6lUwf96DHYFR+Hivf+/t8DCUBf9mlbDYE9H1LH5/3sIjhw5gmHDhiEhIbftoEGD8MMPP8DR0bHMYyci8bBAICLR6evqYGBzRwxs7oi7z1Kx+9Jj7P33W8rVp3LvVWjhZI6+Tavj3Ub2MNWXaztkokpLEARcepiIfaGP8efVaKRm5gAAJBLgnbrWGNTCEZ3q2xY4Elnt2rWRmpoKd3d3LFu2DO3atSvj6ImoLLBAIKIyVcfGGLN71McnXVxw4nYsdgU/wpk7zxH8IBHBDxIx748b6FTfBv2aVkdbF2vIeQkSUal4EJeGfZefYP/lx3iUkKFZXs1MHwObO6J/8+qoZqafZ52nT5/i6NGjGDVqFACgXr16OHXqFDw9PSGT8SMEUWXFv24i0gpdmRTdGtqjW0N7xCRn4mDYE+wLfYLw2FQcvhaDw9diYGGoi96NHdC7iQOaOppxHHWiYop7kYUj12OwP/QxQqOSNMsNdXXQ3d0e/ZpVg3cty3wjjGVnZ2PJkiX45ptvkJaWBnd3dzRv3hwA0LJly7J8C0SkBSwQiEjr7Ez1ML5tbYx7xxk3o1OwL/QJDoY9RdyLLPhdeAC/Cw9QzUwfPRvbo1cjBzRwMGGxQFSI5HQl/G9E48+r0bgQGQ/Vv8MQSSVAm7rW6NesGrq42UFft+Abio8cOYLp06fjzp07AABvb2/N/AZEVDWwQCCickMikaCBgykaOJhiVndXnL0bhwOXn+Cfm7F4kpSBtafvYe3pe6hlZYiejezRs5EDXOw4CRNRaqYS/9yKxR9XonE24jmUKkHzmns1U/Ru7ID3mji8dojhyMhIzJgxA3/88QcAwNbWFosXL8awYcMglfJSP6KqhAUCEZVLMh0p2rvYoL2LDTKVKpy8/Qx/XH2K47ee4X5cGpafuIvlJ+7C2doQ3RrYoWsDOzSqbsozC1RlJKRl45+bsfC/EYNzd+OQnaPWvOZqZ4xejR3wrrt9kUYIUyqVaNu2LZ48eQKZTIZp06Zh7ty5MDExEfMtEFE5xQKBiMo9PbmOZm6FF1k5OP7vN6Vn7jzHvedpWHUqEqtORcLeVA9dG9ihSwNbeDpZcI4FqnSeJGXg7xsx8L8eg+AHCZpJzADA2doQvRo5oFdj+zxDkxZGEHJXlkgkkMvlmDNnDvbu3YulS5eifv36Yr0FIqoAWCAQUYVipJDhvSbV8F6TakjNVOJk+HMcvR6Dk+HPEJ2cqblnwdxAnnsGwtUGLWuZaTtsohJRC8DVx8k4czcBJ24/w7UnyXleb+BgknsGraEd6toYFfkM2tWrVzF16lRMnToV/fr1AwCMHTsW48aN41k4ImKBQEQVl7GePHeUo8YOyFSqcP5uHPyvx+DYrVgkpiux7/IT7Lv8BDpSCWoZ6eCpyQN0bmCH2tZF/yBFVNZSM5U4FxGHf27F4O9rOki9GKh5TSIBWtS0QNeGdujiZgtHC4NibTshIQFff/01Vq1aBbVajWfPnqFv376QSCS8z4CINFggEFGloCfXQcf6tuhY3xY5KjWCHyTiZPgznLj9DHefvcDdFAkWHb2DRUfvoIaFAdrUtUKbutbwqW3JidlIq9RqATeepuDs3ec4FxGH4AcJr9xkLIGhQgfv1LVGe9fce3KsjYs/opBKpcLGjRsxe/ZsxMfHAwD69++PH3/8kcUyEeXDAoGIKh2ZjhQ+tS3hU9sSs3vUR2RsMlbtP41nMhsE3k9EVEI6tgdGYXtgFKQSoLGjGdrUtUabulZo4mjGydlIdE+SMnAu4jnORsThQmQ8EtKy87zubGWItvWsoJ90D5MGdIKhfsmHGb106RI++ugjhISEAADc3NywbNkydOzY8a3eAxFVXiwQiKjSq2FhgHfsBfTo4YFstQQBkfE4dzcOZyJyb3K+HJWEy1FJWHY8AkYKGZo7mcOrliW8nS3QsJopCwZ6a9HJGQi8l4DA+/EIvJeAe3FpeV43Usjg7WyJNnWt8E49a9SyMoRSqcThw5HQlb3d/peQkICQkBCYmppi/vz5mDhxIuRynjUjosKxQCCiKsVQIUMnN1t0crMFkPtN7vmI3GLh/N04JKYrcSr8OU6FPwcAGOjqwKOmObyd/79gUMgKnmCKCMgdHehxYgaCHyTg4r14BN5PwMP49DxtpBKgiaMZWotw5io7OxtXr17VzHzcpUsXrFixAgMGDICNjU2p9EFElRsLBCKq0qqZ6WNgC0cMbOEItVrAzegUBN5PQOC/H+ySM5Q4GxGHsxFxAABdHSkaVjNBsxrmaFbTHM1qmMPOtPDJp6jyy1SqcP1JMkKjEhH6MAmhUYl4lpqVp41UAjSsZgqvWhbwqmWJFrUsRLn35ejRo5g2bRqePn2K8PBw2NvbAwAmTZpU6n0RUeXFAoGI6F9SqQQNq5miYTVTfNi6FtRqAeGxqZpiIeh+AuLTshEalYTQqCTg3H0AuUVG0xpmaFTdVLO+iR4v4aiMVGoB956/wLUnybj2JBmXo5Jw42lynpmLAUAmlaBBNVN4O1vAu5YlPJzMRd0n7t27h5kzZ+LgwYMAABsbG0RERGgKBCKi4mCBQERUCKlUgvr2Jqhvb4KRrWpBEAREJaQj5GGi5tvi2zEpeJKUgSdJGfjzarRm3VpWhmhYzRTu1UzQsJop6tuZwNxQV4vvhopLqVLj3vM03HiaWwxce5yMm9EpSM9W5WtrZaSb56xSo+qm0JOLfylaeno6FixYgB9++AFZWVnQ0dHBlClTMG/ePJiamorePxFVTiwQiIiKSCKRoKalIWpaGqJfs+oAgBdZObj6KAmXHyXh2uPcD5JPkjJwPy4N9+PS8MeVp5r1bU0UcLEzgaudMVztjOFiZ4w6Nka8p0HLBEFATEombsek4nZ0KsJjUnA7JhWRz1/kOzMAAPpyHTRwyC38GjuawqOGBRwt9Mt8uNDMzEy4u7vj3r17AICOHTti2bJlcHNzK9M4iKjyYYFARPQWjBQytKxjhZZ1rDTLEtKyce1JMq7/+63z9afJeJyYgdiULMSmPMeZO881baWS3FGWnK2N4GxlmPvT2hDO1oawNlJwjPpSlKlU4X5cGu49T8O95y9wL+7fn8/TkJqVU+A6RgoZXO2M/z0bZIpG1U3hbG0EHan2fy96enro06cPfv/9d/z888/o168f9xciKhWiFgjfffcd/vrrL4SFhUFXVxdJSUlvXEcQBMyfPx/r1q1DYmIivLy8sHLlSjRo0EDMUImISo2FoS7a1rNG23rWmmWpmUrciX2B2zEpCI9Jxe2YVITHpCI5Q4kH8el4EJ+OE//ZjrFCBkcLAzha6MPR3ACOFgao8e/z6uYGZXIJS0WiVgt4/iILUQnpeJSQjkcJGXiU+PLf6YhOyYSQ/4QAAEBHKoGzlSFc/j2742pnAhc7Y1Q3L/szA4VJSkrCvHnzMHLkSDRp0gQAMH/+fHzzzTcwMCjejMpERK8jaoGQnZ2NAQMGwMfHBxs3bizSOosXL8bPP/8MPz8/1KtXD99++y06d+6M8PBwGBsbixkuEZFojPXk8KhpDo+a5pplgiDgWWoWIv/9Fvve8zTci8v996PEdKRm5eBmdApuRqcUuE0zAznsTPRga6KX+9P0358mClgaKWBpqAsLQ10Y6OqUmw+5JZGjUiMhPRsJadlIeJGN5y+yEJOciZiUTMSmZCImOROxKVl4lppZ4CVBrzLRk6G2jRGcrXLP1NS2zj1rU9PSoNxe6qVWq7FhwwbMmjULcXFxCA0NxenTpyGRSGBkZKTt8IioEhK1QJg/fz4AwM/Pr0jtBUHAkiVL8OWXX6Jfv34AgC1btsDW1hY7duzA+PHjxQqViKjMSSQS2P77Ab9lbas8r2UqVbnffCf++014QnruN+OJGXickFs8JKUrkZSuxO2Y1Nf2o5BJYWWkgIWhLswNdWGsJ4OJngzGenIYK2Qw0ZfDWE8GI4UMenKdfx/S3J+y3H8rZDqQSnO/aZdKJNCRSqDzStEhCAJyVGqoBAFqNaASBKjUucsyc9TIVKr+faiRpVQhM0eFtCwVUjNzkJqpzPMzJTMHyRnZiE/LLQqS0pVFzqmOVAIHM73cMy7m/559sTBAdXMD1LQ0gKWhboUqlsLDw/HNN99oZkGuX78+5syZU6HeAxFVPOXqHoT79+8jJiYGXbp00SxTKBRo27YtLly4UGCBkJWVhays/x9vOiUl95s2pVIJpbLo/6lQ0bzMKXNb+phb8VTE3OoAcLLQg5OFHlA772uCICAlMwexKbnfnMekZOX+OzX357PULCSkKZGQlo2sHDWyctSakZbEIIEOpgUcE2Xbmj4kgJm+HBaGurAy0oWtce6ZktxH7r/tTPRgbaQL2WsmHMvJKfheg/ImJiYGs2bNwvbt2wEAJiYmmDNnjmYW5Iq0L5dXrx4XmM/SVRGPuRVFWeW0XBUIMTExAABbW9s8y21tbfHw4cMC11mwYIHmTMWrTp48yWsyRXTsmLgfBqoy5lY8lTW3hgCcATjLAFj8+wAgCEC2GnihBFKVwIscCdKVQIYKyFQB6TkSZKqAzJzcZVkqCZRqQKnOXU/5ykNA4d9Yv+41AJBJBMilyPfQlQL6MgH6OoCeDLk/dQToywB9GWAkA4zkAozlgIEMkEpyALxS5KgAJALqRCAauY/K4vDhw5rioEOHDvD19YW5uXml3Ye1ITIyEgAQGBiIuLg4LUdTOXF/LX3p6elvblQKil0gzJs3r8AP5K8KDg7WTPFeEv89dSoIQqGnU2fNmoWZM2dqnqekpMDR0RHt27eHpaVliWOggimVShw7dgydO3eGXM6JoEoTcyse5vbtCIKAHLUAtVr499IhQP3vJURZ2UqcPn0a7du1hUJXFzpSaC5BkkokkEklkJaDEX8qgsTERJib596j0qVLF7x48QKNGzfG5MmTud+KICgoCADg5eUFT09PLUdTufCYK574+Pgy6afYBcLkyZMxePDg17ZxcnIqUTB2dnYAcs8kvDr747Nnz/KdVXhJoVBAoVDkWy6Xy7lTioj5FQ9zKx7mtuQKm+JNqVTCRBewNTNkbkvowYMHmDlzJq5cuYIbN25AT08Pcrkcfn5+OHz4MPdbkbzMKfMrHua29JVVPotdIFhZWcHKyurNDUugVq1asLOzw7Fjx9C0aVMAuSMhnT59GosWLRKlTyIiIm3IyMjAokWLsGjRImRmZkJHRwdnzpzJcx8eEZE2FH4nVymIiopCWFgYoqKioFKpEBYWhrCwMLx48ULTxtXVFfv37weQe2nR9OnT8f3332P//v24fv06Ro4cCQMDAwwZMkTMUImIiMqEIAjYu3cv6tevj/nz5yMzMxPt27dHWFgYiwMiKhdEvUl57ty52LJli+b5y7MCJ0+eRLt27QDkDuGWnJysafPZZ58hIyMDEydO1EyU9vfff3MOBCIiqvDS0tLw3nvv4fjx4wAAR0dH/PTTT+jfvz+HLiWickPUAsHPz++NcyAI/5nWUiKRYN68eZg3b554gREREWmBoaEh9PT0oFAo8Nlnn+GLL77giHtEVO6Uq2FOiYiIKhO1Wo2tW7eie/fusLGxAQCsXLkSKpUKzs7OWo6OiKhgot6DQEREVFUFBwejZcuWGDlyJL788kvN8po1a7I4IKJyjQUCERFRKXr27Bk+/PBDeHp6IjAwEMbGxqhfv762wyIiKjJeYkRERFQKlEolVq1aha+//loz+Mbw4cOxcOHCPHP7EBGVdywQiIiISsGiRYswZ84cAECzZs2wfPlytGzZUstREREVHy8xIiIiKqFXR+KbNGkS6tevj3Xr1iEoKIjFARFVWDyDQEREVEwZGRn44YcfEBwcjEOHDkEikcDc3BzXr1+HVMrv3oioYmOBQEREVESCIODgwYOYMWMGHjx4AAA4fvw4OnXqBAAsDoioUuCRjIiIqAhu376Nbt26oW/fvnjw4AGqV6+OXbt2oWPHjtoOjYioVLFAICIieo309HR88skncHd3x99//w1dXV18+eWXuH37NgYNGgSJRKLtEImIShUvMSIiInoNuVyOw4cPIycnB7169cIvv/yC2rVrazssIiLRsEAgIiL6j8uXL6NBgwbQ1dWFXC7HunXrkJqaiu7du2s7NCIi0fESIyIion89f/4c48aNg4eHB5YuXapZ3rp1axYHRFRl8AwCERFVeTk5OVi9ejXmzp2LpKQkAMC9e/e0GxQRkZawQCAioirt1KlTmDJlCq5fvw4AaNKkCVasWIFWrVppOTIiIu3gJUZERFRlLV68GO3bt8f169dhYWGB1atX49KlSywOiKhKY4FARERVVu/evaFQKDBx4kTcuXMHH330EXR0dLQdFhGRVvESIyIiqhIEQcAff/yBq1ev4quvvgIAuLq64uHDh7C1tdVydERE5QcLBCIiqvTCw8Mxbdo0HD16FFKpFD179kSTJk0AgMUBEdF/8BIjIiKqtFJTU/HZZ5/B3d0dR48ehVwux2effYY6depoOzQionKLZxCIiKjSEQQB27Ztw2effYaYmBgAQI8ePbBkyRLUrVtXy9EREZVvLBCIiKjSSUpKwrRp05CYmIjatWtjyZIl6Nmzp7bDIiKqEFggEBFRpZCUlARTU1NIJBKYm5vjxx9/RGxsLGbOnAmFQqHt8IiIKgzeg0BERBVaTk4OVq5cCWdnZxw6dEizfPTo0Zg1axaLAyKiYmKBQEREFdaZM2fg4eGByZMnIzExEZs3b9Z2SEREFR4LBCIiqnAeP36MDz74AG3btsXVq1dhbm6OlStX4vfff9d2aEREFR7vQSAiogpl48aNmDp1KtLT0yGRSDBu3Dh8++23sLKy0nZoRESVAgsEIiKqUBwcHJCeno5WrVph+fLlaNq0qbZDIiKqVFggEBFRuRYREYFbt26hd+/eAIDu3bvjn3/+QYcOHSCRSLQcHRFR5cN7EIiIqFx68eIFvvjiCzRo0AC+vr6IjY3VvNaxY0cWB0REIhG1QPjuu+/QsmVLGBgYwMzM7I3tlUolPv/8c7i7u8PQ0BAODg4YPnw4nj59KmaYRERUjgiCgB07dsDFxQWLFi2CUqlEy5YtkZWVpe3QiIiqBFELhOzsbAwYMAATJkwoUvv09HSEhoZizpw5CA0Nxb59+3Dnzh3NaWUiIqrcwsLC8M4772Do0KF4+vSpZm6Dw4cPo0aNGtoOj4ioShD1HoT58+cDAPz8/IrU3tTUFMeOHcuzbPny5fD09ERUVBT/cyAiqsRiY2Ph5eWF7OxsGBgYYPbs2fj444+hp6en7dCIiKqUcn+TcnJyMiQSSaGXKGVlZeU57ZySkgIg93IlpVJZFiFWKS9zytyWPuZWPMyteN42t4IgaO4lsLCwwPjx4xETE4OFCxfC0dHxrbZd0XG/Fder+WWOSxf3XfGUVU4lgiAIYnfi5+eH6dOnIykpqVjrZWZmonXr1nB1dcW2bdsKbDNv3jzNmYpX7dixAwYGBiUJl4iIysDNmzexadMmTJ48GU5OTgAAtVoNqZTjZ5D4IiMj8fHHH+Onn35C7dq1tR0OUZGkp6djyJAhSE5OhomJiWj9FPsMQmEfyF8VHByM5s2blzgoILdCGjx4MNRqNVatWlVou1mzZmHmzJma5ykpKXB0dET79u1haWn5VjFQfkqlEseOHUPnzp0hl8u1HU6lwtyKh7kVT0ly++TJE8yePRs7d+4EAPzzzz/Yt2+fmGFWSNxvxRUUFAQA8PLygqenp5ajqVy474onPj6+TPopdoEwefJkDB48+LVtXn4TVFJKpRIDBw7E/fv3ceLEiddWSAqFAgqFIt9yuVzOnVJEzK94mFvxMLfiKUpus7KysGTJEnzzzTdIS0uDRCLBmDFj8N133/H38hrcb8XxMqfMr3iY29JXVvksdoFgZWUl6nT2L4uDiIgInDx5kmcBiIgqgWPHjmHSpEmIiIgAAHh7e2P58uVvfbaZqKLKzMzE8+fPtR2GKNRqNRwdHfH06VNeMlgC1tbWWh+cQdSblKOiopCQkICoqCioVCqEhYUBAOrUqQMjIyMAgKurKxYsWIC+ffsiJycH/fv3R2hoKP7880+oVCrExMQAyL15TVdXV8xwiYhIJDdu3EBERARsbW2xePFiDBs2jB8cqMrKzMzEs2fPUK1aNejo6Gg7nFKnVqthamoKExMT/p0Xk0qlwpMnT2BjY6PVIkHUAmHu3LnYsmWL5nnTpk0BACdPnkS7du0AAOHh4UhOTgYAPH78GIcOHQIANGnSJM+2Xl2HiIjKt7S0NERFRaF+/foAgEmTJiErKwsTJkwQ9cY6oorg+fPnlbY4oLejo6ODatWq4enTp5qR3LRB1ALBz8/vjXMgvDqIkpOTE8pgUCUiIhKJIAjYvXs3PvnkE+jp6eH69etQKBSQy+X4/PPPtR0eUbnB4oAKUx72DZ73ISKiUnH16lW0b98egwcPxuPHj5GTk4MHDx5oOywiIiomFghERPRWUlNTMX36dDRt2hSnT5+Gvr4+/ve//+HmzZtwcXHRdnhERFRM5X4mZSIiKr8eP36MiRMnIjU1FQAwYMAA/PDDD6hZs6aWIyMiopLiGQQiIiqxatWqoW7dunBzc8Px48exe/duFgdEVC49evQI7dq1g5ubGxo1aoQ9e/ZoO6Ryi2cQiIioxCQSCaZPn473338fBgYG2g6HiKhQMpkMS5YsQZMmTfDs2TM0a9YMPXr0gKGhobZDK3d4BoGIiN6KiYkJZ0slqkJWrlwJJycnyGQyjB07FjY2NsUakKB///74+eefxQuwEPb29pph9G1sbGBhYYGEhIQyj6MiYIFAREREREVy/fp1TJ8+HStXrsSjR49gbGyMXr16wcnJqcjbmDt3Lr777jukpKSIF+gbXLp0STPjc0ktWLAALVq0gLGxMWxsbNCnTx+Eh4eXYpTawwKBiIiIiIrk0KFD8PDwwLvvvgszMzNs3rwZY8aMKdY2GjVqBCcnJ2zfvl2kKF8vPj4ew4cPx7p1695qO6dPn8akSZNw8eJFHDt2DDk5OejSpQvS0tJKKVLtYYFARERERG9Uu3ZtfPnllwgMDIREIoGNjQ1kMhl8fHzytNu5cyfs7Ozw5MkTzbIxY8agUaNGSE5OBgD07t0bO3fuLNX4du7cCT09vdf2m5WVhb59+2LWrFlo2bLlW/Xn7++PkSNHokGDBmjcuDE2b96MqKgohISEFDme8ooFAhERERG9UUBAAJydnfHDDz8gOjoaAwcORPPmzfO1Gzx4MOrUqYOFCxcCAObPn4+jR4/iyJEjMDU1BQB4enoiKCgIWVlZ+db//vvvYWRk9NrH2bNnC+zXxcUFCxYsKLBfQRAwcuRIdOjQAb6+vqWZGgDQfOi3sLAoUjzlGUcxIiIiItISQRCQoVRppW99uQ4kEkmR2xsZGeHBgwdo3bo17OzsEB8fDwcHh3ztJBIJvvrqK4wcORLVqlXD0qVLcfbsWVSrVk3Tplq1asjKykJMTEy+oZE/+ugjDBw48LWxvLqtV/v97rvv0L9/fzg4OOTr9/z58/jtt9/QqFEjHDhwAACwdetWuLu7FzkHhREEATNnzkTr1q3RsGHDIsVTnrFAICIiItKSDKUKbnOPaqXvm//rCgPdon8UvHr1KgBoPlBnZGRAT0+vwLbdunWDm5sb5s+fj7///hsNGjTI87q+vj4AID09Pd+6FhYWmm/hi6tnz56F9tu6dWuo1epC1503bx7mz5//2u0HBwcXeNZk8uTJuHr1Ks6dO1fkeMozFghERERE9EZhYWGoU6eOZt4AKysrJCYmFtj2+PHjuH37NlQqFWxtbfO9/nJ4UWtr63yvff/99/j+++9fG8uRI0fQpk2bfMuPHj362n5fZ/LkyRg8ePBr2xQ0WtOUKVNw6NAhnDlzBtWrVy+1eLSJBQIRERGRlujLdXDzf1211ndxhIWFoXHjxprnTZs2xbZt2/K1Cw0NxahRo7B69Wrs3r0bc+bMyTdr8fXr11G9enVYWVnlW7+klxiFhoZiwIABWLt2LXbt2lVgv69jZWVVYDyFEQQBU6ZMwf79+3Hq1CnUqlWrVOPRJhYIRERERFoikUiKdZmPNoWFhaF3796a5127dsWsWbOQmJgIc3NzAMCDBw/Qq1cvTJs2Db6+vmjYsCFatGiBkJAQeHh4aNY9e/YsunTpUmA/JbnE6MGDB3j33XfxxRdfwNfXF25ubgX2W5omTZqEHTt24ODBgzA2NkZMTAwAwNTUFLGxsWUeT2niKEZERERE9FpqtRrXrl3LcwbB3d0dzZs3x+7duwHkXjbUvXt39OrVCx9//DEAwMPDA7169cKXX36pWS8zMxP79+/H2LFjSyW2l/327t0bs2fPLrTf0rZ69WokJyejXbt2sLe31zxWr16tlXhKU8UoWYmIiIhIa6RSaYETgM2ZMweffPIJxo4dCwsLC9y6dQtqtTrPLMkHDx7Ms87GjRvh5eUFb2/vUontZb//9d9+S5sgCIW+NnPmzHzLxI6nNLFAICIiIqIS6dGjByIiIvDkyRM4OjoWaR25XI7ly5eLHBm9DRYIRERERFRi06ZNK1b7cePGiRQJlRbeg0BERERERBosEIiIiIiISIMFAhERERERabBAICIiIiIiDRYIRERERESkwQKBiIiIiIg0WCAQEREREZEGCwQiIiIiItJggUBERERERBosEIiIiIjotdq1a4fp06cDAJycnLBkyRKtxvOSn58fzMzMRO9HIpHgwIEDovdTXsi0HQARERERVRzBwcEwNDTUdhgAgEGDBqFHjx6ltr158+bhwIEDCAsLy7M8Ojoa5ubmpdZPeSfqGYTvvvsOLVu2hIGBQYmqu/Hjx0MikZSbKpWIiIioqrO2toaBgYG2w4BSqYS+vj5sbGxE78vOzg4KhUL0fsoLUQuE7OxsDBgwABMmTCj2ugcOHEBgYCAcHBxEiIyIiIiISuK/lxhJJBJs2LABffv2hYGBAVxcXHD48OE869y8eRM9evSAkZERbG1t4evri7i4OM3r/v7+aN26NczMzGBpaYmePXsiMjJS8/qDBw8gkUiwe/dutGvXDnp6eti2bVu+S4ycnJwgkUjyPV76/PPPUa9ePRgYGMDZ2Rlz5syBUqkEkHu50vz583HlyhXNen5+fpr3+OolRteuXUOHDh2gr68PS0tLjBs3Di9evNC8PnLkSPTp0wc//vgj7O3tYWlpiUmTJmn6Ku9ELRDmz5+PGTNmwN3dvVjrPXnyBJMnT8b27dshl8tFio6IiIiofEhLSyv0kZmZWeS2GRkZRWpb2ubPn4+BAwfi6tWr6N69O8aPH4+EhAQAuZfntG3bFk2aNMGlS5fg7++P2NhYDBw4ME+cM2fORHBwMI4fPw6pVIq+fftCrVbn6efzzz/H1KlTcevWLXTt2jVfHMHBwYiOjkZ0dDQeP34Mb29vtGnTRvO6sbEx/Pz8cPPmTSxduhTr16/HL7/8AiD3cqWPP/4YDRo00Gxj0KBB+fpIT09Ht27dYG5ujuDgYOzZswf//PMPJk+enKfdyZMnERkZiZMnT2LLli3w8/PTFBzlXbm7B0GtVsPX1xeffvopGjRo8Mb2WVlZyMrK0jxPSUkBkHvaqaJUaRXJy5wyt6WPuRUPcyse5lY8zK24Xs1vWedYrVbn++BrZGRUaPvu3bvjzz//1Dy3sbFBenp6gW3btm2LEydOaJ47OTnl+ab+JZVKVdywIQiCJu5X/w0AI0aM0HyY/vbbb7FixQoEBgaie/fuWLVqFZo2bYpvv/1W037Dhg2oWbMmbt++jXr16qFv3755+lq/fj3s7Oxw/fp1NGzYUNPXtGnT0KdPH027l8tf/rS0tNS8Nn36dERHRyMwMFDz+uzZszWv16hRAzNnzsTu3bvxySefQKFQwNDQEDKZLM9lS6/2oVarsXXrVmRkZMDPzw+GhoZwc3PDsmXL8N5772HBggWwtbWFIAgwNzfHsmXLoKOjg3r16qFHjx74559/8OGHH74x12q1usD9sqz21XJXICxatAgymQxTp04tUvsFCxZg/vz5+ZafPHmyXFwfV1kdO3ZM2yFUWsyteJhb8TC34mFuxfHy8pXAwMACP0CLydHREaampkVun5OTo/kCtLhtBUEosF1Rt/fqdrOzs5GSkgK1Wo3MzMw826hTp06e50ZGRnj06BFSUlIQGBiIU6dOwcTEJN92r127Bjs7O9y/fx/fffcdLl26hISEBM2H8tu3b6NGjRqay3dcXV3z9JOZmQlBEPK9Hz8/P2zatAlHjhyBQqHQvH7w4EGsXr0a9+/fR1paGnJycmBsbKx5PSsrCyqVqsD8ZGRkICUlBVevXkWDBg3ytHN3d4darUZoaChatWoFpVKJevXq5TlbY2lpiZs3bxYp9/Hx8flulAZQaGFY2opdIMybN6/AD+SvCg4ORvPmzYsdTEhICJYuXYrQ0NA814u9zqxZszBz5kzN85SUFDg6OqJ9+/Z5qkgqHUqlEseOHUPnzp15+VcpY27Fw9yKh7kVD3MrrqCgIACAl5cXPD09y7Tvp0+f5vuw/LoPjTo6OtDT09M8j4mJKbStVCqFvr6+5vn9+/cLbFfcUYhkMhl0dXVhYmICqVQKPT29PO/BxMRE81wQBEgkkjzte/bsiYULF+bbrr29PQwNDTF06FBUr14d69evh4ODA9RqNRo1agSZTAYTExPNGRYbG5s8/erp6UEikeRZdurUKXz++efYvn07WrVqpVl+8eJFfPjhh5g3bx66dOkCU1NT/Pbbb/j555816ysUCujo6BRYzOjr68PExARyuRxyuTxPm5eFmJGRkabNy/YvKRQKSKXSArf9X5aWlgVeoh8fH//GdUtDsQuEyZMnY/Dgwa9t4+TkVKJgzp49i2fPnqFGjRqaZSqVCh9//DGWLFmCBw8e5FtHoVAUeFf5y18eiYP5FQ9zKx7mVjzMrXiYW3G8zKk28iuVSiGV5r0N1NjYuMjri9X2TSQSiSbuV/8N5H1Pr156JJVK4eHhgb1798LZ2RkyWf6PnvHx8bh16xbWrl2ruV/g3Llzebb7ctv/zd2rywHg7t27GDBgAGbPno3+/fvn6ScgIAA1a9bEV199pVkWFRWVZ32FQgGVSpXv9/Nq3w0aNMCvv/6KjIwMTaEVEBAAqVQKV1dXSKVSzU3Or27n5ZffBW27oL4K2i/Lal8tdoFgZWUFKysrMWKBr68vOnXqlGdZ165d4evri1GjRonSJxERERGJZ9KkSVi/fj0++OADfPrpp7CyssLdu3exa9curF+/Hubm5rC0tMS6detgb2+PqKgofPHFF8XuJyMjA7169UKTJk0wbty4PGda7OzsUKdOHURFRWHXrl1o0aIF/vrrL+zfvz/PNpycnHD//n2EhYWhevXqMDY2zvdF9NChQ/H1119jxIgRmDdvHp4/f44pU6bA19cXtra2JUtSOSPqKEZRUVEICwtDVFQUVCoVwsLCEBYWlmcYKFdXV80vx9LSEg0bNszzkMvlsLOzg4uLi5ihEhEREZEIHBwccP78eahUKnTt2hUNGzbEtGnTYGpqqvlWfteuXQgJCUHDhg0xY8YM/PDDD8XuJzY2Frdv38aJEyfg4OAAe3t7zQMA3nvvPcyYMQOTJ09GkyZNcOHCBcyZMyfPNt5//31069YN7du3h7W1NXbu3JmvHwMDAxw9ehQJCQlo0aIF+vfvj44dO2LFihUlS1A5JOpNynPnzsWWLVs0z5s2bQog9wbidu3aAQDCw8ORnJwsZhhERERE9BZOnTql+fd/L/ku6Ebohw8f5rnWvm7duti3b1+h2+/UqRNu3rxZ6HadnJwK7GfkyJEYOXLka9u8avHixVi8eHGeZdOnT9f8W6FQ4Pfff8+33n+36+7unme0qP8qaDjTijTxr6gFQlHGe33TL7Kg+w6IiIiIiEgcol5iREREREREFQsLBCIiIiIi0mCBQEREREREGiwQiIiIiIhIgwUCERERERFpsEAgIiIiKmMqlUrbIVA5VR72DRYIRERERGXI2toaT548KRcfBKl8UalUePLkCaytrbUah6jzIBARERFRXnp6erCxsUF0dPQb54OqiNRqNeLj42FpaQmplN9FF5eNjQ309PS0GgMLBCIiIqIypqenh+rVq2s7DFEolUqEhYXB3d0dcrlc2+FQCbCsIyIiIiIiDRYIRERERESkwQKBiIiIiIg0WCAQEREREZFGpbtJ+eVoAKmpqbwxRgRKpRLp6elISUlhfksZcyse5lY8zK14mFtxvXjxQvMzJSVFy9FULtx3xZOamgoAoo9+JREq2fha9+7dQ+3atbUdBhERERGRKCIjI+Hs7Cza9ivdGQQLCwsAQFRUFExNTbUcTeWTkpICR0dHPHr0CCYmJtoOp1JhbsXD3IqHuRUPcysu5lc8zK14kpOTUaNGDc3nXbFUugLh5YQcpqam3ClFZGJiwvyKhLkVD3MrHuZWPMytuJhf8TC34hF7AjrepExERERERBosEIiIiIiISKPSFQgKhQJff/01FAqFtkOplJhf8TC34mFuxcPcioe5FRfzKx7mVjxlldtKN4oRERERERGVXKU7g0BERERERCXHAoGIiIiIiDRYIBARERERkQYLBCIiIiIi0qgQBcKqVatQq1Yt6OnpwcPDA2fPnn1t+9OnT8PDwwN6enpwdnbGmjVr8rXZu3cv3NzcoFAo4Obmhv3794sVfrlWnNzu27cPnTt3hrW1NUxMTODj44OjR4/maePn5weJRJLvkZmZKfZbKXeKk9tTp04VmLfbt2/nacf9Nldxcjty5MgCc9ugQQNNG+63uc6cOYNevXrBwcEBEokEBw4ceOM6PN4WTXFzy+Nt8RQ3vzzmFl1xc8tjbtEsWLAALVq0gLGxMWxsbNCnTx+Eh4e/cb2yOuaW+wLht99+w/Tp0/Hll1/i8uXLaNOmDbp3746oqKgC29+/fx89evRAmzZtcPnyZcyePRtTp07F3r17NW0CAgIwaNAg+Pr64sqVK/D19cXAgQMRGBhYVm+rXChubs+cOYPOnTvj8OHDCAkJQfv27dGrVy9cvnw5TzsTExNER0fneejp6ZXFWyo3ipvbl8LDw/PkrW7duprXuN/mKm5uly5dmienjx49goWFBQYMGJCnHfdbIC0tDY0bN8aKFSuK1J7H26Irbm55vC2e4ub3JR5z36y4ueUxt2hOnz6NSZMm4eLFizh27BhycnLQpUsXpKWlFbpOmR5zhXLO09NT+Oijj/Isc3V1Fb744osC23/22WeCq6trnmXjx48XvL29Nc8HDhwodOvWLU+brl27CoMHDy6lqCuG4ua2IG5ubsL8+fM1zzdv3iyYmpqWVogVVnFze/LkSQGAkJiYWOg2ud/metv9dv/+/YJEIhEePHigWcb9Nj8Awv79+1/bhsfbkilKbgvC423RFCW/POaWTEn2XR5zi+bZs2cCAOH06dOFtinLY265PoOQnZ2NkJAQdOnSJc/yLl264MKFCwWuExAQkK99165dcenSJSiVyte2KWyblVFJcvtfarUaqampsLCwyLP8xYsXqFmzJqpXr46ePXvm+8arsnub3DZt2hT29vbo2LEjTp48mec17rels99u3LgRnTp1Qs2aNfMsr+r7bUnweFt2eLwVB4+54uMxt2iSk5MBIN/f+KvK8phbrguEuLg4qFQq2Nra5llua2uLmJiYAteJiYkpsH1OTg7i4uJe26awbVZGJcntf/30009IS0vDwIEDNctcXV3h5+eHQ4cOYefOndDT00OrVq0QERFRqvGXZyXJrb29PdatW4e9e/di3759cHFxQceOHXHmzBlNG+63b7/fRkdH48iRIxgzZkye5dxvS4bH27LD423p4jG3bPCYWzSCIGDmzJlo3bo1GjZsWGi7sjzmyorVWkskEkme54Ig5Fv2pvb/XV7cbVZWJc3Dzp07MW/ePBw8eBA2Njaa5d7e3vD29tY8b9WqFZo1a4bly5dj2bJlpRd4BVCc3Lq4uMDFxUXz3MfHB48ePcKPP/6Id955p0TbrMxKmgc/Pz+YmZmhT58+eZZzvy05Hm/Fx+Nt6eMxt2zwmFs0kydPxtWrV3Hu3Lk3ti2rY265PoNgZWUFHR2dfFXPs2fP8lVHL9nZ2RXYXiaTwdLS8rVtCttmZVSS3L7022+/4cMPP8Tu3bvRqVOn17aVSqVo0aJFlfpW4G1y+ypvb+88eeN++3a5FQQBmzZtgq+vL3R1dV/btirutyXB4634eLwtOzzmli4ec4tmypQpOHToEE6ePInq1au/tm1ZHnPLdYGgq6sLDw8PHDt2LM/yY8eOoWXLlgWu4+Pjk6/933//jebNm0Mul7+2TWHbrIxKklsg95uskSNHYseOHXj33Xff2I8gCAgLC4O9vf1bx1xRlDS3/3X58uU8eeN++3a5PX36NO7evYsPP/zwjf1Uxf22JHi8FRePt2WLx9zSxWPu6wmCgMmTJ2Pfvn04ceIEatWq9cZ1yvSYW6xbmrVg165dglwuFzZu3CjcvHlTmD59umBoaKi5G/6LL74QfH19Ne3v3bsnGBgYCDNmzBBu3rwpbNy4UZDL5cLvv/+uaXP+/HlBR0dHWLhwoXDr1i1h4cKFgkwmEy5evFjm70+bipvbHTt2CDKZTFi5cqUQHR2teSQlJWnazJs3T/D39xciIyOFy5cvC6NGjRJkMpkQGBhY5u9Pm4qb219++UXYv3+/cOfOHeH69evCF198IQAQ9u7dq2nD/TZXcXP70rBhwwQvL68Ct8n9Nldqaqpw+fJl4fLlywIA4eeffxYuX74sPHz4UBAEHm/fRnFzy+Nt8RQ3vzzmFl1xc/sSj7mvN2HCBMHU1FQ4depUnr/x9PR0TRttHnPLfYEgCIKwcuVKoWbNmoKurq7QrFmzPENAjRgxQmjbtm2e9qdOnRKaNm0q6OrqCk5OTsLq1avzbXPPnj2Ci4uLIJfLBVdX1zwHhaqkOLlt27atACDfY8SIEZo206dPF2rUqCHo6uoK1tbWQpcuXYQLFy6U4TsqP4qT20WLFgm1a9cW9PT0BHNzc6F169bCX3/9lW+b3G9zFfeYkJSUJOjr6wvr1q0rcHvcb3O9HPqxsL9xHm9Lrri55fG2eIqbXx5zi64kxwUec9+soJwCEDZv3qxpo81jruTfIImIiIiIiMr3PQhERERERFS2WCAQEREREZEGCwQiIiIiItJggUBERERERBosEIiIiIiISIMFAhERERERabBAICIiIiIiDRYIRERERESkwQKBiIhKzZkzZ9CrVy84ODhAIpHgwIEDb1xn3rx5kEgkeR52dnbiB0tERAVigUBERKUmLS0NjRs3xooVK4q1XoMGDRAdHa15XLt2TaQIiYjoTWTaDoCIiMrGzp07MWrUKERGRqJatWoAgDFjxiAoKAhnz56FqanpW/fRvXt3/F/7dg/SOhiFcfwJiItOcRAyVKRgQegQgwiCOBdJEVFpB3F1DiKiKAhRZ8HF1Uno0LFU6NTFQcWlKMSvwUURB9HBQXq3F7lqsd7We7n9/yBD4P04GR/OSSqVqntfW1sbXQMA+EfQQQCAFpHJZJRIJLS5uSlJWltbU7FYVKFQeBcONjY21NnZWfMpl8sNqy2KIjmOo97eXmUyGV1eXjbsbABAfeggAECLsCxL6+vrmpyclOM42traUrlcNt2Et+bm5jQ9PV3zvI/2fcfQ0JB2d3fV19en29tbhWGo4eFhVSoVdXV1NeQOAMDXWdVqtfq3iwAA/JyBgQFVKhXt7+9rdHS0afdYlqV8Pq/x8fG69j0/Pysej2thYUFBEDSnOADApxgxAoAWUiwWdXZ2ptfXV3V3d3+67qdHjN7q6OhQMplUFEVNOR8AUBsjRgDQIo6PjzU1NaWdnR3t7e1pZWVFuVzuw7U/OWL0u5eXF52enmpkZKQp5wMAaiMgAEALuL6+1tjYmBYXFzUzM6P+/n4NDg7q6OhInue9W2/btmzbrvuep6cnnZ+fm/erqyudnJzItm3FYjFJ0vb2tvL5vEqlkiRpfn5evu8rFovp7u5OYRjq8fFRs7Oz3/xaAMCfYMQIAP5zDw8PSqVSSqfTWlpakiR5niff97W8vNzQuw4PD+W6rlzXlSQFQSDXdbW6umrW3N/f6+Liwrzf3Nwom80qkUhoYmJC7e3tOjg4UE9PT0NrAwB8DT8pAwAAADDoIAAAAAAwCAgAAAAADAICAAAAAIOAAAAAAMAgIAAAAAAwCAgAAAAADAICAAAAAIOAAAAAAMAgIAAAAAAwCAgAAAAADAICAAAAAIOAAAAAAMD4BSBxlMi46D4wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.ekf_internal as ekf_internal\n",
    "ekf_internal.show_linearization()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the curve above is the process model, then the dotted lines shows the linearization of that curve for the estimate $x=1.5$.\n",
    "\n",
    "We linearize systems by taking the derivative, which finds the slope of a curve:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "f(x) &= x^2 -2x \\\\\n",
    "\\frac{df}{dx} &= 2x - 2\n",
    "\\end{aligned}$$\n",
    "\n",
    "and then evaluating it at $x$:\n",
    "\n",
    "$$\\begin{aligned}m &= f'(x=1.5) \\\\&= 2(1.5) - 2 \\\\&= 1\\end{aligned}$$ \n",
    "\n",
    "Linearizing systems of differential equations is similar. We linearize $f(\\mathbf x, \\mathbf u)$, and $h(\\mathbf x)$ by taking the partial derivatives of each to evaluate $\\mathbf F$ and $\\mathbf H$ at the point $\\mathbf x_t$ and $\\mathbf u_t$. We call the partial derivative of a matrix the [*Jacobian*](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant). This gives us the the discrete state transition matrix and measurement model matrix:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F \n",
    "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n",
    "\\mathbf H &= \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "This leads to the following equations for the EKF. I put boxes around the differences from the linear filter:\n",
    "\n",
    "$$\\begin{array}{l|l}\n",
    "\\text{linear Kalman filter} & \\text{EKF} \\\\\n",
    "\\hline \n",
    "& \\boxed{\\mathbf F = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n",
    "\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)}  \\\\\n",
    "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q  & \\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n",
    "\\hline\n",
    "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}} \\\\\n",
    "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z - \\boxed{h(\\bar{x})}\\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n",
    "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
    "\\end{array}$$\n",
    "\n",
    "We don't normally use $\\mathbf{Fx}$ to propagate the state for the EKF as the linearization causes inaccuracies. It is typical to compute $\\bar{\\mathbf x}$ using a suitable numerical integration technique such as Euler or Runge Kutta. Thus I wrote $\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)$. For the same reasons we don't use $\\mathbf{H\\bar{x}}$ in the computation for the residual, opting for the more accurate $h(\\bar{\\mathbf x})$.\n",
    "\n",
    "I think the easiest way to understand the EKF is to start off with an example. Later you may want to come back and reread this section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Tracking a Airplane\n",
    "\n",
    "This example tracks an airplane using ground based radar. We implemented a UKF for this problem in the last chapter. Now we will implement an EKF for the same problem so we can compare both the filter performance and the level of effort required to implement the filter.\n",
    "\n",
    "Radars work by emitting a beam of radio waves and scanning for a return bounce. Anything in the beam's path will reflects some of the signal back to the radar. By timing how long it takes for the reflected signal to get back to the radar the system can compute the *slant distance* - the straight line distance from the radar installation to the object.\n",
    "\n",
    "The relationship between the radar's slant range distance $r$ and elevation angle $\\epsilon$ with the horizontal position $x$ and altitude $y$ of the aircraft is illustrated in the figure below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This gives us the equalities:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\epsilon &= \\tan^{-1} \\frac y x\\\\\n",
    "r^2 &= x^2 + y^2\n",
    "\\end{aligned}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "We want to track the position of an aircraft assuming a constant velocity and altitude, and measurements of the slant distance to the aircraft. That means we need 3 state variables - horizontal distance, horizontal velocity, and altitude:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}=    \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Process Model\n",
    "\n",
    "We assume a Newtonian, kinematic system for the aircraft. We've used this model in previous chapters, so by inspection you may recognize that we want\n",
    "\n",
    "$$\\mathbf F = \\left[\\begin{array}{cc|c} 1 & \\Delta t & 0\\\\\n",
    "0 & 1 & 0 \\\\ \\hline\n",
    "0 & 0 & 1\\end{array}\\right]$$\n",
    "\n",
    "I've partioned the matrix into blocks to show the upper left block is a constant velocity model for $x$, and the lower right block is a constant position model for $y$.\n",
    "\n",
    "However, let's practice finding these matrices. We model systems with a set of differential equations. We need an equation in the form \n",
    "\n",
    "$$\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{w}$$\n",
    "where $\\mathbf{w}$ is the system noise. \n",
    "\n",
    "The variables $x$ and $y$ are independent so we can compute them separately. The differential equations for motion in one dimension are:\n",
    "\n",
    "$$\\begin{aligned}v &= \\dot x \\\\\n",
    "a &= \\ddot{x} = 0\\end{aligned}$$\n",
    "\n",
    "Now we put the differential equations into state-space form. If this was a second or greater order differential system we would have to first reduce them to an equivalent set of first degree equations. The equations are first order, so we put them in state space matrix form as\n",
    "\n",
    "$$\\begin{aligned}\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} &= \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \n",
    "\\dot x\\end{bmatrix} \\\\ \\dot{\\mathbf x} &= \\mathbf{Ax}\\end{aligned}$$\n",
    "where $\\mathbf A=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$. \n",
    "\n",
    "Recall that $\\mathbf A$ is the *system dynamics matrix*. It describes a set of linear differential equations. From it we must compute the state transition matrix $\\mathbf F$. $\\mathbf F$ describes a discrete set of linear equations which compute $\\mathbf x$ for a discrete time step $\\Delta t$.\n",
    "\n",
    "A common way to compute $\\mathbf F$ is to use the power series expansion of the matrix exponential:\n",
    "\n",
    "$$\\mathbf F(\\Delta t) = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t  + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A \\Delta t)^3}{3!} + ... $$\n",
    "\n",
    "\n",
    "$\\mathbf A^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$, so all higher powers of $\\mathbf A$ are also $\\mathbf{0}$. Thus the power series expansion is:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n",
    "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}\\Delta t\\\\\n",
    "\\mathbf F &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is the same result used by the kinematic equations! This exercise was unnecessary other than to illustrate finding the state transition matrix from linear differential equations. We will conclude the chapter with an example that will require the use of this technique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The measurement function takes the state estimate of the prior $\\bar{\\mathbf x}$ and turn it into a measurement of the slant range distance. We use the Pythagorean theorem to derive:\n",
    "\n",
    "$$h(\\bar{\\mathbf x}) = \\sqrt{x^2 + y^2}$$\n",
    "\n",
    "The relationship between the slant distance and the position on the ground is nonlinear due to the square root. We linearize it by evaluating its partial derivative at $\\mathbf x_t$:\n",
    "\n",
    "$$\n",
    "\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x})}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}\n",
    "$$\n",
    "\n",
    "The partial derivative of a matrix is called a Jacobian, and takes the form \n",
    "\n",
    "$$\\frac{\\partial \\mathbf H}{\\partial \\bar{\\mathbf x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "In other words, each element in the matrix is the partial derivative of the function $h$ with respect to the $x$ variables. For our problem we have\n",
    "\n",
    "$$\\mathbf H = \\begin{bmatrix}{\\partial h}/{\\partial x} & {\\partial h}/{\\partial \\dot{x}} & {\\partial h}/{\\partial y}\\end{bmatrix}$$\n",
    "\n",
    "Solving each in turn:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x} &= \\frac{\\partial}{\\partial x} \\sqrt{x^2 + y^2} \\\\\n",
    "&= \\frac{x}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial \\dot{x}} &=\n",
    "\\frac{\\partial}{\\partial \\dot{x}} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial y} &= \\frac{\\partial}{\\partial y} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= \\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "giving us \n",
    "\n",
    "$$\\mathbf H = \n",
    "\\begin{bmatrix}\n",
    "\\frac{x}{\\sqrt{x^2 + y^2}} & \n",
    "0 &\n",
    "&\n",
    "\\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "This may seem daunting, so step back and recognize that all of this math is doing something very simple. We have an equation for the slant range to the airplane which is nonlinear. The Kalman filter only works with linear equations, so we need to find a linear equation that approximates $\\mathbf H$. As we discussed above, finding the slope of a nonlinear equation at a given point is a good approximation. For the Kalman filter, the 'given point' is the state variable $\\mathbf x$ so we need to take the derivative of the slant range with respect to $\\mathbf x$. For the linear Kalman filter $\\mathbf H$ was a constant that we computed prior to running the filter. For the EKF $\\mathbf H$ is updated at each step as the evaluation point $\\bar{\\mathbf x}$ changes at each epoch.\n",
    "\n",
    "To make this more concrete, let's now write a Python function that computes the Jacobian of $h$ for this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def HJacobian_at(x):\n",
    "    \"\"\" compute Jacobian of H matrix at x \"\"\"\n",
    "\n",
    "    horiz_dist = x[0]\n",
    "    altitude   = x[2]\n",
    "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
    "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's provide the code for $h(\\bar{\\mathbf x})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    \"\"\" compute measurement for slant range that\n",
    "    would correspond to state x.\n",
    "    \"\"\"\n",
    "    \n",
    "    return (x[0]**2 + x[2]**2) ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write a simulation for our radar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class RadarSim:\n",
    "    \"\"\" Simulates the radar signal returns from an object\n",
    "    flying at a constant altityude and velocity in 1D. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, dt, pos, vel, alt):\n",
    "        self.pos = pos\n",
    "        self.vel = vel\n",
    "        self.alt = alt\n",
    "        self.dt = dt\n",
    "        \n",
    "    def get_range(self):\n",
    "        \"\"\" Returns slant range to the object. Call once \n",
    "        for each new measurement at dt time from last call.\n",
    "        \"\"\"\n",
    "        \n",
    "        # add some process noise to the system\n",
    "        self.vel = self.vel  + .1*randn()\n",
    "        self.alt = self.alt + .1*randn()\n",
    "        self.pos = self.pos + self.vel*self.dt\n",
    "    \n",
    "        # add measurement noise\n",
    "        err = self.pos * 0.05*randn()\n",
    "        slant_dist = math.sqrt(self.pos**2 + self.alt**2)\n",
    "        \n",
    "        return slant_dist + err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Process and Measurement Noise\n",
    "\n",
    "The radar measures the range to a target. We will use $\\sigma_{range}= 5$ meters for the noise. This gives us\n",
    "\n",
    "$$\\mathbf R = \\begin{bmatrix}\\sigma_{range}^2\\end{bmatrix} = \\begin{bmatrix}25\\end{bmatrix}$$\n",
    "\n",
    "\n",
    "The design of $\\mathbf Q$ requires some discussion. The state $\\mathbf x= \\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are position (down range distance) and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of $\\mathbf Q$. The third element of  $\\mathbf x$ is altitude, which we are assuming is independent of the down range distance. That leads us to a block design of $\\mathbf Q$ of:\n",
    "\n",
    "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & 0 \\\\ 0 & \\mathbf Q_\\mathtt{y}\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "`FilterPy` provides the class `ExtendedKalmanFilter`. It works similarly to the `KalmanFilter` class we have been using, except that it allows you to provide a function that computes the Jacobian of $\\mathbf H$ and the function $h(\\mathbf x)$. \n",
    "\n",
    "We start by importing the filter and creating it. The dimension of `x` is 3 and `z` has dimension 1.\n",
    "\n",
    "```python\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "```\n",
    "We create the radar simulator:\n",
    "```python\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "```\n",
    "We will initialize the filter near the airplane's actual position:\n",
    "\n",
    "```python\n",
    "rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
    "```\n",
    "\n",
    "We assign the system matrix using the first term of the Taylor series expansion we computed above:\n",
    "\n",
    "```python\n",
    "dt = 0.05\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "```\n",
    "\n",
    "After assigning reasonable values to $\\mathbf R$, $\\mathbf Q$, and $\\mathbf P$ we can run the filter with a simple loop. We pass the functions for computing the Jacobian of $\\mathbf  H$ and $h(x)$ into the `update` method.\n",
    "\n",
    "```python\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    rk.predict()\n",
    "```\n",
    "\n",
    "Adding some boilerplate code to save and plot the results we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d+Vmcp9QkDnPnzsXHx4e+ffs6lA8ePJjKlSsTGhrKzp07mThxItu2bSMmJgaAM2fOEByc97234OBgzpw5c9XzZWZmOixhnpycDIDVas3z/l1Ru3y+4j7vrULxKzjFrnAUv4JT7ApH8Ss4xa5wLn9O+mv8Ro8ezZgxY/D09GTz5s3UqVOH1QfOczIxg7Je7txZPQiLmwtLdp9lxqrDHIhPA6Bb3RD+eV89PMyut/y/ibPuvfycr9QkDp988gmDBw/Gw8Mx2xw5cqT9+3r16lG9enWaNm3K5s2bady4MYDDu3SX/fUdu796/fXXmTJlSp7ypUuX4uXlVdDLKJTLyZAUjOJXcIpd4Sh+BafYFY7iV3CKXf4dP36cX375hd9//533338fX19fe11gYCDDhw/nrrvuwsfHhzEzl7D01J9z9FhcDFxdID0797OZp6tB30o2mvmcYnnMqWK/Fmcq7nsvPT39htuWisTht99+Y9++fXz11VfXbdu4cWPMZjMHDhygcePGhIaGcvbs2Tztzp07R0hIyFWPM3HiRMaPH2/fTk5OJiIigqioKIcfhOJgtVqJiYmhS5cumM16py+/FL+CU+wKR/ErOMWucBS/glPsCu7pp5+2T0Rz9OhRnnvuOYf6tl3u5r3lhzh8Oo1Npy4C0L56ECcS0zl8Ph1sEOxjYWCzCjzUsiK+nrdX/J11711+q+ZGlIrEYdasWTRp0oSGDRtet+2uXbuwWq2EhYUB0KpVK5KSkvjjjz9o3rw5ABs2bCApKYnWrVtf9TgWiwWLxZKn3Gw2O+0XiTPPfStQ/ApOsSscxa/gFLvCUfwKTrG7tvPnz1O2bFnc3P78KDl27Fjee+89LBYLNpvNIX4JqZkMm7uZg/F/LuI2sXstRrevimEYbD6eiDXHoFmlAFxdrv5GyO2guO+9/JzLqYlDamoqBw8etG8fOXKErVu3EhAQQMWKFYHcLOibb77h7bffzrP/oUOH+Pzzz+nRowdBQUHs3r2bCRMm0KhRI/sgm9q1a9OtWzdGjhzJzJkzgdzpWHv27KmB0SIiIiL5sHfvXt58803mz5/P/PnzadOpOz9tj+OuWsFUqVKFDz77D+fTsqnXtBVz1x4lIS2LkxfS+e3gec6lZBLm58HTXWtSPdiH+hVyV4U2mUw0iQxw8pXJjXBq4rBp0yY6duxo3778atDQoUOZM2cOAF9++SWGYTBw4MA8+7u7u/Prr7/y7rvvkpqaSkREBHfffTeTJk3C1dXV3u7zzz/niSeeICoqCoDevXszffr0IrwyERERkVvPsWPH7J/R3vz0J7J2luFCWhav/7KHCv6eHE2wABY4vD3PvqG+Hsx7pIXWXSjFnJo4dOjQAcMwrtlm1KhRjBo16op1ERERrFq16rrnCQgIYN68eQXqo4iIiMjt6PTp0xiGQfny5e1lXbp0oUaNGiSYy3GmRl9IyyLQ252EtCyOJqTj7uZCgDmHiiEBBPlY8Pdyp5yPhSaR/jSrFICH2fUaZ5SSrlSMcRARERGR4nHq1CkmTJjAt99+y4gRI/jwww8BSM3MZv6G49w/+RN+3p9KUkY2vRqG88/7G7DrdDJnky/RspIfvy2PoUePZhojcgtS4iAiIiIidj4+PixcuJDs7Gw+++wzxj43mYMXc/jX0n2cuJBhb9cwoiz/vL8BHmZXmkT6A1r/4lanxEFERETkNnX06FGOHz/OnXfeaS/z9fXl3uGPszzODe+qTbn7w1h7XfmynrSuGkiOzeDZ7rX06tFtRomDiIiIyG3GarXywAMP8OOPP1K5cmX279+Pq6srO08lMX35QVZ7tcOtKmQCZlcTtcN8aVU1kMc7VsPXQ68g3a6UOIiIiIjcZsxmMxkZGRiGweEjR5n4yWK2pJThwH/XWTCZoEf9MIa3rkS98n56siCAEgcRERGRW9q+ffuIiYlhzJgxDuVjxoxh1/FzhNw7ka8PAaTi7upCt3qhjLmrGjVCfJzSXym5lDiIiIiI3KJGjRrFxx9/DEDnzp2pVauWvS6kXmuCBrxBQoYVXw83xnepwb2NK+DnqVeR5MpcnN0BERERESka/5sozJgxA4CsbBtTY/Yz8OMNXMyw0rCCH8smtGdYm8pKGuSalDiIiIiIlHLbtm3jb3/7G8nJyfYya46Nu/oMoE7jFvzrX2/zj0mT+HzDMTr8cwXv/XqAHJtBzwZhzB/VkmAfDyf2XkoLvaokIiIiUor961//4umnnwagTp06jB07liPn0xgyawMnEzOgy4vEuPrw+5d72Hz8IgDBPhZe7FmHXg3DndhzKW30xEFERESkFOvWrZv9+88++4wNhxPoP3MdJxMzMLuaANh7JoXNxy/i5e7Kiz3rsPqZjkoaJN/0xEFERESkhDMMgw0bNjB9+nSGDRtG586d7XX16tXjkUceoWaDJuzyvoP+H60HoFaoD5+NaIG7qwtfbzrB4fOpPNahGhEBXs66DCnllDiIiIiIlHDLli0jKioKgIsXLzokDtYcGw+Me5kpP+3m1KkEXF1M9G8WwTNda1LWyx2AkXdWcUq/5daixEFERESkhDEMA5PJZN/u2LEjERERnDhxgj/++IPk5GTKlPHh280neWvJPs6lZAJQOcibGQ82plaor7O6LrcwJQ4iIiIiJYBhGKxcuZLp06dTtWpV3nrrLXudm5sbr776KhcybATXb8fLS46w7nBC7uBnIKiMO/c2Ks/YTtXx9dCUqlI0lDiIiIiIlACJiYl0796dzMxMypYty6RJk8DNwpy1RzmWkMaRtKpsPJoIh/fY9/Fyd+XJTtUZ3qYy7m6a80aKlhIHERERESfIyMjA09PTvh0QEMCgQYOYPXs2np6e/PD7dmZszeDEhQyH/e6IKEvLKoG0qBJAs0oBlLHo45wUD91pIiIiIsXEMAwWL15MdHQ0J0+eZNu2bQ5jGSZMmEBUVBS1WnVm8KxNpGXlUL6sJwOaRRDkY6FDzXKE+Xle4wwiRUeJg4iIiEgxMZlMvPrqq2w+Y8W31UPUefEX2tYI4aFWkbSrXo7atetwzq0co+ZtJS0rh1ZVAvnooSb4aNyClABKHERERESKyIkTJ4iIiHAoq9/v75w87QFARjbE7D5LzO6z9GtagdhjiRw6lwZAzRAfZippkBJEo2hEREREbrIlS5bQsWNHKlWqxLFjxwDIzM7hp22nWRyXmzQ81Koi/3m0FQOb5yYWX286yaFzaZSxuDGibWW+GNlCMyRJiaInDiIiIiI32R9//MHKlSsBmDZjFr6t+vHVxhNkZtsAGNAsgim962EymWhaKYCWVQKZ/8dxutQJpV/TCnrKICWSnjiIiIiIFMKmTZtIT093KBs5ciRms5lqjduwxKUZn647Rma2jQBvdwY2j2BKn7oOg6L73FGeL0e1YkTbykoapMRS4iAiIiJSAL///jstW7akWbNmfPnllw51oaGhrFm/kUqDXyXD5kKtUB++GNmC2P/rzOt9G2Bxc3VSr0UKzqmJw+rVq+nVqxfh4eGYTCa+//57h/phw4ZhMpkcvlq2bOnQJjMzk7FjxxIUFIS3tze9e/fm5MmTDm0SExMZMmQIfn5++Pn5MWTIEC5evFjEVyciIiK3MrPZzIYNGwCIjo7GMAx7XVpmNtO3ZnIgPpUQXwufjmhO66pBDk8ZREobpyYOaWlpNGzYkOnTp1+1Tbdu3YiLi7N//fLLLw7148aN47vvvuPLL79kzZo1pKam0rNnT3JycuxtBg0axNatW1m8eDGLFy9m69atDBkypMiuS0RERG4dhmHw22+/sXPnTofy5s2b06xZMxo0aMBjjz2GzWbjyPk0pi8/wP0frmP1/nN4mF34YHBjgn08nNR7kZvHqYOju3fvTvfu3a/ZxmKxEBoaesW6pKQkZs2axWeffUbnzp0BmDdvHhERESxbtoyuXbuyZ88eFi9ezPr162nRogUAH3/8Ma1atWLfvn3UrFnz5l6UiIiI3DIOHTrEfffdx7Zt2+jXrx9fffWVQ/2iRYsICAjAZDKxJy6ZBz5cR2pmNgD+XmZmDWtG44r+zui6yE1X4mdVWrlyJcHBwZQtW5b27dvz6quvEhwcDEBsbCxWq5WoqCh7+/DwcOrVq8fatWvp2rUr69atw8/Pz540ALRs2RI/Pz/Wrl171cQhMzOTzMxM+3ZycjIAVqsVq9VaFJd6VZfPV9znvVUofgWn2BWO4ldwil3hKH4F99fYhYSEEBcXB8CCBQs4evQo5cuXt7f38fFhf1wSm09c5N1fD5KamU3dcB+61w2lV4NQwst63lb/Drr3Cs5ZscvP+Up04tC9e3ceeOABIiMjOXLkCC+++CJ33XUXsbGxWCwWzpw5g7u7O/7+jpl8SEgIZ86cAeDMmTP2RON/BQcH29tcyeuvv86UKVPylC9duhQvL69CXlnBxMTEOOW8twrFr+AUu8JR/ApOsSscxe/G2Ww2tm3bRnJyMu3bt3eIXfv27dm2bRs9evRg06ZNbNu2DYDN500sPOHC+Ut/jlsI8TR4sHwiXqmJbF27h63FfSElhO69givu2P11RrBrKdGJQ//+/e3f16tXj6ZNmxIZGcnChQvp27fvVfczDMNh8NGVBiL9tc1fTZw4kfHjx9u3k5OTiYiIICoqCl9f3/xeSqFYrVZiYmLo0qULZrOmaMsvxa/gFLvCUfwKTrErHMUvf6xWK82bN2fXrl2UK1eO1q1b06NHD3vsoqKicHP78yOTYRhErzjE3AOHATC7mrgjoix3VPBjWOtIgn0sTrmOkkD3XsE5K3aX36q5ESU6cfirsLAwIiMjOXDgAJA71VlWVhaJiYkOTx3i4+Np3bq1vc3Zs2fzHOvcuXOEhIRc9VwWiwWLJe8PvtlsdtoPgjPPfStQ/ApOsSscxa/gFLvCUfxujNlspm7duuzatYtz586xbt06+vTpY4+dq6sbO08nseNUEi2rBLJwexzRK3KThtHtqzD2ruqUsZSqj1RFTvdewRV37PJzrlJ1lyckJHDixAnCwsIAaNKkCWazmZiYGPr16wdAXFwcO3fu5K233gKgVatWJCUl8ccff9C8eXMANmzYQFJSkj25EBERkVtfTk4OP//8M8uWLSM6OtqhbuzYscTHx/Poo4/aP0jZbAY/bT/NtJj9HE3IfZ3D1cVEji132tVJveowvE3l4r0IESdyauKQmprKwYMH7dtHjhxh69atBAQEEBAQwOTJk7nvvvsICwvj6NGjPP/88wQFBXHvvfcC4Ofnx4gRI5gwYQKBgYEEBATw1FNPUb9+ffssS7Vr16Zbt26MHDmSmTNnAjBq1Ch69uypGZVERERuI3379uXHH38EYMiQIfY/KAK0bduWFStWYLVa+eWXXzibfImnv93FusMJAHi7u1I1uAzbTyYB8FiHqkoa5Lbj1MRh06ZNdOzY0b59eUzB0KFDmTFjBjt27ODTTz/l4sWLhIWF0bFjR7766it8fHzs+0ybNg03Nzf69etHRkYGnTp1Ys6cObi6/rki4+eff84TTzxhn32pd+/e11w7QkRERG49ffr0sScO8+fPd0gcAI4lpPHW4r0s3+3KpfWrMQzwcnfl8Y7VGNa6Et4WNzYevUBc0iV6NQhzxiWIOJVTE4cOHTo4rLL4V0uWLLnuMTw8PIiOjs7zyPF/BQQEMG/evAL1UUREREoPq9XKggUL+PDDD5k/f77DWlADBw5k8eLFDBs2jG7dutnLE1IziV5+kM83HMOaYwC5k6fUK+/LuwMaUbVcGXvbZpUCiu1aREqaUjXGQURERORaXnvtNSZPngzkLvj64osv2us8PT35+uuv7dt74pKZFrOfFfvi/5swwJ3VA2lsOcsDPToR7u99zRkYRW43Ls7ugIiIiEhBGIaBzWZzKBs2bBguLrkfb3777ber7jfn9yP0ef93lu4+izXHoGEFP+aNaMGsh5pQ2QeCfSxKGkT+Qk8cREREpFTJyMjgyy+/ZPr06Tz99NMMGDDAXhcZGckbb7xB06ZN6dChg8N+OTaDg/Gp/HPJXpbtiQegc+1gnulWixohueMnteKxyNUpcRAREZFSZcOGDTz88MMATJ8+3SFxAHj66afz7PPD1lNM+nEXF9NzEwN3Nxde6FGbh1pF6smCyA1S4iAiIiIlls1mIy0tzWFGxfbt29sXbMvMzCQlJcWh/n9lZOUw+cddfLXpBJA7S1Ljiv4836M2dcJ9i+UaRG4VShxERESkxElPT+ff//43H3zwAa1atWL27Nn2OpPJxLvvvouPj0+eKVX/1/rDCbz4/U4OxKdiMsHYjtV4olN13Fw1xFOkIJQ4iIiISIljGAb/+Mc/SEpK4ujRo/zrX/8iMDDQXt+pUyeHtkkZVk5cyOD4hXT2nUlm1f5zbPvvYm3lfCy82/8OWlcLKvbrELmVKHEQERERp8rOzubw4cPUqFHDXubt7c3DDz/MtGnTaN26NefOnXNIHHaeSuLzDcdYuussielZ2K6wLJS7qwv9mlVgXOcaBJWxFMeliNzSlDiIiIiIUxiGwRtvvMEHH3yAyWTi8OHDuLn9+dFkwoQJjBgxgrp163I2+RITF+zgkjWHjKwcFu86k+d45XwsRPh7UinQm+aVA7irVjDBvh7FeUkitzQlDiIiIuIUJpOJdevWcfLkSQB++ukn7r33Xnt9+fLlKV++PMv3nuWZ/2znfGrW/+wLvRqEM6B5BFXLlcHXw4ynu2uxX4PI7USJg4iIiBS5jIwMli9fzt133+1Q/vjjj7Nw4UJ69epFhQoVgNz1FqKXHyD2WCIZWTlsOpYIQO0wX7rXCyUxPYv7m1SgbrhfsV+HyO1MiYOIiIgUqejoaKZMmUJCQgI7duygXr169rouXbpw+PBhIiMjAcjOsTHhm238sPW0vY3Z1cSw1pWYEFUTD7OeKog4ixIHERERKVImk4mEhAQA3n//fWbMmGGvc3FxsScNaZnZPPnlVpbtOYubi4nxUTXwsbjRrno5KgV5O6XvIvInTWQsIiIiN0VSUhLvvfceFy5ccCh/6KGHCAwMZPDgwQwfPtxebrMZZGTlcCEtiyW7ztD3g7Us23MWdzcX3h/cmMc6VGNIq0pKGkRKCD1xEBERkUL75ptvGD58OGlpaVitViZMmIDNZrD3TAqnL2bw/sKNWNzdyfaxsPbgef65dB9bjl/Mc5xAb3c+eqgpTSL9i/8iROSalDiIiIhIodWvX5+0tDQA3v/gA7ya9OGT349yLiXzhvb39zIzsHlFHm5bWWsuiJRQShxERETkhsXHx/Pvf/+bFi1aOKzeXKtWLe65ty9lQytStkVf3ly8DwBvd1eqBudOl2pgcDIxg7PJl+jVIJyxd1UnoIw7Hm4uuLnq7WmRkk6Jg4iIiNyQbdu20bx5c7KysoiKiqLNnR34ePVhKgV5UzPUhwstx7DlQjrsSQbg/+6uzZBWkVjcHGdCMgwDk8nkjEsQkUJQ4iAiIiI3pH79+lSoUIHDhw/z64qVPPLJWtYcyU0SXF1M5NgMXF1MlCtj4e9dqtO/WcUrHkdJg0jppMRBREREHBw7dowZM2ZgNpt5+eWX7eWpWTn0e2ISO08nkxFUmzVHkrG4uWAywSWrjcYVyzJraDP8vd2d2HsRKSpKHERERMQuIyOD+vXrk5KSQpkyZXjqqac4nGTj8w3H+WnbaTKzA8EUCAmXsLi58OGQJlQPLsPGoxfoXi9MC7SJ3MKUOIiIiNzG/jrewN3iQdRDT7Bw4UJcfALpFb2G46l/to8I8KR+eT/aVAuiS50Qgn08AKjg71XcXReRYqbEQURE5Da0e/du3n//fdatX8+bny1k+d5z1Cvvy+KdZ9hUphUh/VsBcDwV3N1c6NkgjMEtImlcsazGKIjcppw699nq1avp1asX4eHhmEwmvv/+e3ud1Wrl2WefpX79+nh7exMeHs5DDz3E6dOnHY7RoUMHTCaTw9eAAQMc2iQmJjJkyBD8/Pzw8/NjyJAhXLx4sRiuUEREpGT62/jn+HzrBeLqP8TIT2OZ/8dxXvhuJ78dOI+H2YWq5byJDPTiqagarJ/Yian97qBJpL+SBpHbmFOfOKSlpdGwYUOGDx/Offfd51CXnp7O5s2befHFF2nYsCGJiYmMGzeO3r17s2nTJoe2I0eO5KWXXrJve3p6OtQPGjSIkydPsnjxYgBGjRrFkCFD+Omnn4roykREREqO5ORkfH197duxxy6Q0HQUZbNzkwA3k437mkSy7eRFAKb1v4PaYb5XOpSI3Macmjh0796d7t27X7HOz8+PmJgYh7Lo6GiaN2/O8ePHqVjxzynevLy8CA0NveJx9uzZw+LFi1m/fj0tWrQA4OOPP6ZVq1bs27ePmjVr3qSrERERKVm2bNnC9OnT+eabb9ixYwfVqlXj+y2neOY/28nKMVHOnMWjnWrTu0llyvlotWYRubZSNcYhKSkJk8lE2bJlHco///xz5s2bR0hICN27d2fSpEn4+PgAsG7dOvz8/OxJA0DLli3x8/Nj7dq1V00cMjMzyczMtG8nJ+fOU221WrFarTf5yq7t8vmK+7y3CsWv4BS7wlH8Ck6xK5zLcVu6dCmfffYZrr7BPPnhz1Ro0IYlu+MB6FI7mH/eVw9vi5vDPrc73XuFo/gVnLNil5/zlZrE4dKlSzz33HMMGjTI4XHr4MGDqVy5MqGhoezcuZOJEyeybds2+9OKM2fOEBwcnOd4wcHBnDlz5qrne/3115kyZUqe8qVLl+Ll5ZyZI/76BEbyR/ErOMWucBS/glPsbty5c+fw8fHBw8PDXhYeEUlwn2fxqNmGXSYXdv03aegcbqOH32lW/Xr6aoe77eneKxzFr+CKO3bp6ek33DbficPRo0f57bffOHr0KOnp6ZQrV45GjRrRqlUrh19WN5PVamXAgAHYbDY++OADh7qRI0fav69Xrx7Vq1enadOmbN68mcaNGwNXXqHyesvdT5w4kfHjx9u3k5OTiYiIICoqyiFxKQ5Wq5WYmBi6dOmC2Wwu1nPfChS/glPsCkfxKzjF7sbt3LmTyZMn8/PPP/Puu+8yevRorFYrS5bGsJ6aeNYKAKB1lQBaVgmgWSV/mkb6O7nXJZfuvcJR/ArOWbG7/FbNjbjhxOGLL77gvffe448//iA4OJjy5cvj6enJhQsXOHToEB4eHgwePJhnn32WyMjIAnX8SqxWK/369ePIkSMsX778uh/aGzdujNls5sCBAzRu3JjQ0FDOnj2bp925c+cICQm56nEsFgsWS973Pc1ms9N+EJx57luB4ldwil3hKH4Fp9jdmB9//BGAGTNm8Pjjj5ORlcO8gy7Enj+Hu6sLnwxrRtvqQU7uZemie69wFL+CK+7Y5edcNzQda+PGjZk6dSoPPvggR48e5cyZM8TGxrJmzRp2795NcnIyP/zwAzabjaZNm/LNN98UuPP/63LScODAAZYtW0ZgYOB199m1axdWq5WwsDAAWrVqRVJSEn/88Ye9zYYNG0hKSqJ169Y3pZ8iIiLFYe/evezevduhrFGjRrRp04bw8HAGDBjAtuMX6PfRBmLPu+DqYuLtfg2VNIjITXFDTxxefvll7r777qvWWywWOnToQIcOHXjllVc4cuTIDZ08NTWVgwcP2rePHDnC1q1bCQgIIDw8nPvvv5/Nmzfz888/k5OTYx+TEBAQgLu7O4cOHeLzzz+nR48eBAUFsXv3biZMmGD/JQpQu3ZtunXrxsiRI5k5cyaQOx1rz549NaOSiIiUCqdPn2bo0KEsW7aMe+65h++++86h/ssvv8Rcxp+P1hzjvpkbyLEZlDEbfDikKW1rXP3puohIftxQ4nCtpOGvgoKCCAq6sb9sbNq0iY4dO9q3L48pGDp0KJMnT7Y/er3jjjsc9luxYgUdOnTA3d2dX3/9lXfffZfU1FQiIiK4++67mTRpEq6urvb2n3/+OU888QRRUVEA9O7dm+nTp9/wNYmIiDhTuXLl7E8afvzxR44dO2Z/LTjlkpVv9qTz7992kpaVA0C3uiG09jhFi8oBTuuziNx6CjyrUnx8PPHx8dhsNofyBg0a3PAxOnTogGEYV62/Vh1AREQEq1atuu55AgICmDdv3g33S0RExFm2bt3KoUOHHBZGNZvNPProo3z66ac8/vjj+PvnDm6OPZbIY5/HcjY5d/rwuuG+PNOtFq0rl+WXX045pf8icuvKd+IQGxvL0KFD2bNnj/2Dvclkss9SlJOTc9M7KSIicquz2Wx06dKF5cuXExAQQI8ePfD09LTXP/3007zwwgu4uLhwMD6Vaat2MW/9Maw5BpUCvXi6ay261wvFxcWkOfRFpEjkO3EYPnw4NWrUYNasWYSEhFxzSlMRERG5MS4uLoSHhwNw4cIF5s+fz8MPP2yv9/DwID7lEv9aso9vYk9y+aF8j/qhvHV/Q8pYSs3STCJSSuX7t8yRI0dYsGAB1apVK4r+iIiI3PI2btzI999/zyuvvOLwB7ixY8eyefNmxo4dS79+/Rz2WbLrDM99u53E9NynCZ1rhzC4ZUU61CinP+KJSLHId+LQqVMntm3bpsRBRESkAEaPHs1HH30EQPfu3Wnbtq29rnnz5uzcudMhEUjPyubln3cz/48TANQJ8+Xle+rRRIu4iUgxy3fi8O9//5uhQ4eyc+dO6tWrl2fRiN69e9+0zomIiNxq2rVrZ08c/v3vfzskDoBD0rD95EXGfbmVw+fTMJlg1J1VmNClJu5uN7QMk4jITZXvxGHt2rWsWbOGRYsW5anT4GgREZHcWQHXrVvH9OnTeeutt6hQoYK97oEHHmDW51/TIKo/HhXq0O2d1VjMrjzTtSZtqgWRlpnNFxuOs/rAOdYdSiDbZhDq68HU/g1pXVULuYmI8+Q7cXjiiScYMmQIL774IiEhWlRGRETkr95//33Gjh0LQNWqVXn55ZftdaeSrSS0eJwfzmbD2dP28sH/3kC14DIkpmWRkJZlL+9RP5TX7q1PWS/34rsAEZEryPezzoSEBP7+978raRAREbmKe++9Fze33L/Nfffdd/bpyzOzcxg7fwvJl7KpFOjFyHaV+fDBxgxtFYnJBAfjU0lIy6JSoBeTe9Vhybg7+WBwEyUNIlIi5PuJQ9++fVmxYgVVq1Ytiv6IiIiUCoZhsHr1aqKjo+nbty+DBg2y15UvX57nn3+eqlWr0q9fP0wmE2eSLvH8dzvYdToZfy8zX45qRaifBwDd6oXxtw7V2H82hWybjXbVy2F21TgGESlZ8p041KhRg4kTJ7JmzRrq16+fZ3D0E088cdM6JyIiUlLFxsbSoUMHAI4dO8bAgQMdBjZPnjyZbSeTOJuWw+qtx3hr0V5SMrNxczExtd8d9qThslA/jzxlIiIlSYFmVSpTpgyrVq1i1apVDnUmk0mJg4iI3JJsNhsuLn8+BWjSpAmNGjViy5YtnDx5kjNnzhAWFgbkPo144fudfLHhuMMxGkaU5Y2+9akd5lusfRcRuRkKtACciIjI7cAwDH799Veio6MpW7Ysc+fOtdeZTCZeeeUVLl68yP3334+7e+44hKxsGy//vJsvNhzHZAKzqwsWNxeeiqrJgy0jcXXRYm0iUjppfXoREZGruHTpEgMGDCAhIQGz2cybb75JaGiovb5Hjx4A7DuTwj+XbOOS1UZ8yiX2n00F4K37GtC3ce5UrEoYRKS0u6GRV2+88Qbp6ek3dMANGzawcOHCQnVKRETEGVJSUhy2PT09eeSRRwAIDg7mwIEDefb5euMJek1fw7I98aw5eJ79Z1MJ8HZnxuDGPNA0AlcXk5IGEbkl3NATh927d1OxYkUeeOABevfuTdOmTSlXrhwA2dnZ7N69mzVr1jBv3jzi4uL49NNPi7TTIiIiN9OSJUt499132b59O4cPH7a/dgTw+OOP06RJE+655548E4LE7D7Lswu2YxjQsWY5utcLIyUzmz53hBNUxlLclyEiUqRuKHH49NNP2b59O++//z6DBw8mKSkJV1dXLBaL/UlEo0aNGDVqFEOHDsVi0S9LEREpPWbOnMmiRYsAWLBgAQMGDLDXRUREEBERkWef3aeTeWL+FgwDBjavyGv31nOYVUlE5FZzw2McGjRowMyZM/nwww/Zvn07R48eJSMjg6CgIO644w6CgoKKsp8iIiI3xZEjR6hcubJD2RNPPMF3331HZGTkDR0jKcPKo/NiybDm0K56EC/1qaukQURuefkeHG0ymWjYsCENGzYsiv6IiIgUiZUrV/Lqq6+ybNkyYmNjady4sb2uffv2LF68mM6dO+Pq6ppn38S0LN799QDnUjPx9zKz6Wgixy+kU8Hfk+iBjbRYm4jcFjSrkoiI3Bb27dvHsmXLAIiOjmb27Nn2OpPJRNeuXfPsYxgGK/bF83/f7eR00iWHOoubCx8MbkxZL/c8+4mI3IqUOIiIyC1nx44dlC9fnoCAAHvZgw8+yHPPPUdAQADNmjWzlx89n8ayPWdpUy0IX08z6w4l8G3sSY4mpAEQ99+EoXKQNwObR5CUYSXC34s21YKICPAq3gsTEXEiJQ4iInLL2LZtG+PGjWPlypW89tprTJw40V7n7e3NunXrqFGjhn0F6FMXM+g3cx3xKZlXPaa3uysDm1dkXJcalLHof5sicvvSb0AREbll+Pj4sGrVKgBmzJjB008/jZvbn/+rq1Wrlv37+JRLPDx7I/EpmQSVsZB8yYrNZlAjxIfu9UJpUz2IrGwbtcN88fM05zmXiMjtRomDiIiUSps3byYnJ8fhtaMqVapw9913c+DAAcaMGUNOTo5D4nDZxqMXePzzzcSnZBLsY+G7x9sQVCZ3rILFLe/gaBERucGVo/9XWloaL774Iq1bt6ZatWpUqVLF4Ss/Vq9eTa9evQgPD8dkMvH999871BuGweTJkwkPD8fT05MOHTqwa9cuhzaZmZmMHTuWoKAgvL296d27NydPnnRok5iYyJAhQ/Dz88PPz48hQ4Zw8eLF/F66iIiUAOfOnaNt27Y0adKEp59+Ok/9p59+yu7duxkzZswV1xVae/A8D/57A/EpmdQIKcP8US0pX9YTi5urkgYRkWvI9xOHRx55hFWrVjFkyBDCwsIKNW91WloaDRs2ZPjw4dx333156t966y2mTp3KnDlzqFGjBq+88gpdunRh3759+Pj4ADBu3Dh++uknvvzySwIDA5kwYQI9e/YkNjbWPqXeoEGDOHnyJIsXLwZg1KhRDBkyhJ9++qnAfRcREecIDAzk/PnzAKxatYrt27fToEEDe72/v79D+3Mpmfx24BzpWTnsiUtmweZTZGbbuKtWMNMHNcLLXQ/fRURuRL5/Wy5atIiFCxfSpk2bQp+8e/fudO/e/Yp1hmHwzjvv8MILL9C3b18A5s6dS0hICF988QWjR48mKSmJWbNm8dlnn9G5c2cA5s2bR0REBMuWLaNr167s2bOHxYsXs379elq0aAHAxx9/TKtWrdi3bx81a9Ys9HWIiEjR2LhxI/v27WP48OH2MhcXF8aMGcOHH37I2LFjqVq1qr3uYHwKs9YcpV55X2qF+vLD1lN8tfEEmdk2h+O2r1GOGQ821hMGEZF8yHfi4O/v7zC9XVE5cuQIZ86cISoqyl5msVho3749a9euZfTo0cTGxmK1Wh3ahIeHU69ePdauXUvXrl1Zt24dfn5+9qQBoGXLlvj5+bF27dqrJg6ZmZlkZv45y0ZycjIAVqsVq9V6sy/3mi6fr7jPe6tQ/ApOsSscxa/gsrKymDRpEtu2bcPT05O7777b/iQhM9tG5ba9ebxOFBGB3kz55QBrDiZQ3t+TbSeTyPpLkgBQJ8yH8mU9CS/rQasqAbSvHoSLYcNqzdv2VqB7r+AUu8JR/ArOWbHLz/nynTi8/PLL/OMf/2Du3Ll4eRXd/NVnzpwBICQkxKE8JCSEY8eO2du4u7vneSwdEhJi3//MmTMEBwfnOX5wcLC9zZW8/vrrTJkyJU/50qVLi/S6ryUmJsYp571VKH4Fp9gVjuKXfzYDfOrcSWjDYdgy0xg++X18qzXlaIqJhEzIsuV9TfbyAm3VfG2kWE0kZkJdf4NWIQY1fBMxmRIByDx8mKWHi/VynEb3XsEpdoWj+BVccccuPT39htvmO3F4++23OXToECEhIVSqVAmz2XGKus2bN+f3kNf01zEUhmFcd1zFX9tcqf31jjNx4kTGjx9v305OTiYiIoKoqCh8fX1vtPs3hdVqJSYmhi5duuSJt1yf4ldwil3hKH7XZxgG69at46uvvmLq1Km4urqSkJbFuK+2caJiVy4Pbd4FEP/nfiE+FhpG+HH0fDqRgV480KQ851MzCSxjoWONoEKNv7sV6N4rOMWucBS/gnNW7C6/VXMj8p043HPPPfndpUBCQ0OB3CcGYWFh9vL4+Hj7U4jQ0FCysrJITEx0eOoQHx9P69at7W3Onj2b5/jnzp3L8zTjf1kslivOxmE2m532g+DMc98KFL+CU+wKR/G7urFjxzJ9+nRMZg8Cm3QnzSeC1fvPcz41E3cXg1F3ViU5M4cV++JpUtGfXg3DqRTkTeVAb1xcbu/k4Ebo3is4xa5wFL+CK+7Y5edc+U4cJk2alN9dCqRy5cqEhoYSExNDo0aNgNx3XletWsWbb74JQJMmTTCbzcTExNCvXz8A4uLi2LlzJ2+99RYArVq1IikpiT/++IPmzZsDsGHDBpKSkuzJhYiIOEe3bt34ZNk2AruN5bMDLsApACoFejGgQjIjOlXThw8RkRKiwHPQxcbGsmfPHkwmE3Xq1LF/uM+P1NRUDh48aN8+cuQIW7duJSAggIoVKzJu3Dhee+01qlevTvXq1Xnttdfw8vJi0KBBAPj5+TFixAgmTJhAYGAgAQEBPPXUU9SvX98+y1Lt2rXp1q0bI0eOZObMmUDudKw9e/bUjEoiIsXAMAxWrVpFdHQ0r7zyCrVr1wbgxIV0TvvUolzvp8HkQmSAJ70alqdxZFmaVfRjecwSJ/dcRET+V74Th/j4eAYMGMDKlSspW7YshmGQlJREx44d+fLLLylXrtwNH2vTpk107NjRvn15TMHQoUOZM2cOzzzzDBkZGTz22GMkJibSokULli5dal/DAWDatGm4ubnRr18/MjIy6NSpE3PmzLGv4QDw+eef88QTT9hnX+rduzfTp0/P76WLiEgBfPLJJzzyyCMAhIWF8cyUt/i/H3ayev+53AYmFwa1qMgrferZXz/SjCwiIiVPvhOHsWPHkpyczK5du+x/Ndq9ezdDhw7liSeeYP78+Td8rA4dOmAYxlXrTSYTkydPZvLkyVdt4+HhQXR0NNHR0VdtExAQwLx58264XyIiUngH41OZ8tMuTidWIbjb41y6EMcvF4JYOnUlWTkGbi4maoX50KN+GH9rX/W2H9AsIlLS5TtxWLx4McuWLbMnDQB16tTh/fffd1hPQUREbh+GYbBs2TKio6Pp0LkrbnWjeH/FQfvCa54Nu+MJ2ICsHIPWVQN55Z56VClXxqn9FhGRG5fvxMFms11xoJrZbMZmuzUX0hERkavbcTKJkXPWc3T3FrJt1dl+NBhO7wegXfUg+jeLYPOxi1xMz8LL4sr9TSK4I6KsczstIiL5lu/E4a677uLJJ59k/vz5hIeHA3Dq1Cn+/ve/06lTp5veQRERKXmsVitms5nM7BzGf72VM6nZeFSsb6+v4OfOsz3qcnf9MFxcTPRsEO7E3oqIyM2Q78Rh+vTp9OnTh0qVKhEREYHJZOL48ePUr19f4whERG5hNpuNJUuW8N577+Hm5sZPP/3E+8sPciA+laAy7nSNMBGXmMrDPVrTqlo5XLXOgojILSXfiUNERASbN28mJiaGvXv3YhgGderUsU9/KiIityabzcajjz7K8ePHMZlMfPbrVqavyF134aU+9ehRP+w6RxARkdKswOs4dOnShS5dutzMvoiISAmSkJBAYGCgfdvNzY3HHnuM56e8RkTr3ryy/BQ2AwY0i1DSICJyG7ihxOG9995j1KhReHh48N57712z7RNPPHFTOiYiIs7xyy+/MHXqVDZt2sTJkyc5kWLj5Z93UznImzK1u1FlXF2sNhOZObmDn1++p56zuywiIsXghhKHadOmMXjwYDw8PJg2bdpV25lMJiUOIiKl3Lfffsuvv/4KJheem/Ety1NCSM/KYe2hhP+2MFEnzJd7GoUzpGUlzK4uTu2viIgUjxtKHI4cOXLF70VEpHTbvXs3tWvXdlh8bcSjj/PN9vMEtLyPnxMCgRxaVQnE39vMvjMpPN6xGvc2Kq8F20REbjP5/jPRSy+9RHp6ep7yjIwMXnrppZvSKRERKVorV66kffv21K1bl+XLl9vLNx9P5IklFwjoNAq8A/H3MvP3zjX4dERzPhjchF8ndKBv4wpKGkREbkP5ThymTJlCampqnvL09HSmTJlyUzolIiJFKz4+ntWrVwMQHR0NwIq98Qz8aD3nUzOpFOjFa/fWZ+1znXiyc3W9jiQiIvmfVckwjCv+pWnbtm0EBATclE6JiMjNs3nzZkJDQ+2LdgLce++9lC9fHh8fH7p160Z88iXGfbWVzGwbnWoF897ARnhbCjzxnoiI3IJu+P8K/v7+mEwmTCYTNWrUcEgecnJySE1N5dFHHy2SToqISP7t3LmT0aNHs3btWp555hnefPNNe11Spo035y3iouFBUmYOY+dvISnDSr3yvnw4pImeMIiISB43nDi88847GIbBww8/zJQpU/Dz87PXubu7U6lSJVq1alUknRQRkfwLDg5m06ZNAPz73//muRdeZOHuBL7ceJydp5LztDe7mnj7gTuUNIiIyBXdcOIwdOhQACpXrkzr1q0xm81F1ikREcmfDRs2kJGRQYcOHexlwcHB9O/fny1btjD8b0/y4OzN7IpLsdfXCvWhdpgvvh5unE3OpEeDMGqG+jih9yIiUhrcUOKQnJyMr68vAI0aNSIjI4OMjIwrtr3cTkREil5SUhJdunRh48aNNGzYkC1btji8SvrKP9/hP9vO8eXGE8SnpODvZWbMXdW5t1F5ArzdndhzEREpbW4ocfD39ycuLo7g4GDKli17xcHRlwdN5+Tk3PROiojIlfn5+eHikvtq0bZt21izZg3t2rUDICvbxiNf7GD/2dyZ8KoEeTN7eDMiA72d1l8RESm9bihxWL58uX3GpBUrVhRph0REJC/DMPj999+JjY3lySefdKgbM2YMWVlZjB07lqZNm9rLP/n9CPvPphLo7c4/etWha91QPMyuxd11ERG5RdxQ4tC+ffsrfi8iIsXj7rvvZtGiRbi6unLfffdRoUIFe92gQYMYPHiww9Pgk4npvPfrAQAm9qhNnzvKF3ufRUTk1pLvqTMWL17MmjVr7Nvvv/8+d9xxB4MGDSIxMfGmdk5ERHJdfpKQk5PDJ5984lDn4uJiTxpSLllJSM3k4TkbSc/KoWmkP30bKWkQEZHCy3fi8PTTT5OcnDuN344dOxg/fjw9evTg8OHDjB8//qZ3UETkdmEYBitWrGDo0KFcunTJoe7RRx+lVatWfPrppzz77LN59rXZDKb8tIuGU5bS5JVl7D+bSoivhXcHNsLFJe+4NBERkfzK97KgR44coU6dOgB8++239OrVi9dee43NmzfTo0ePm95BEZHbxdNPP83bb78NQKdOnXjooYfsdeHh4axdu9a+nZ6VzfdbTtM4sixVgsow6cddzP/juL2+rJeZuQ83p3xZz+K7ABERuaXlO3Fwd3cnPT0dgGXLltn/xxYQEGB/EiEiIvl377332hOHr7/+2iFxOJ6Q+3s3IsCTpbvP8tJPuzl1MQNXFxMR/p4cTUjHZIJ/3t+QO2sE4Wl2xcdD6+2IiMjNk+/EoW3btowfP542bdrwxx9/8NVXXwGwf/9+h8F6IiKSl2EYLFu2jOjoaJ5//nlatmxpr2vdujUjRoygc+fO3Hffffby1fvPMWLuRqw5BsE+FuJTMgHw9XAj+VI2RxPS8fcy88Z9DehaN7TYr0lERG4P+R7jMH36dNzc3PjPf/7DjBkzKF8+d9DdokWL6Nat203vYKVKlTCZTHm+Hn/8cQCGDRuWp+5//0cMkJmZydixYwkKCsLb25vevXtz8uTJm95XEZHr+frrr4mKiuKnn34iOjraoc5kMvHvf/+bAQMGkJ4Nz/xnG0/M38Kj82Kx5hgAxKdk4uXuymMdqrJuYidmDW3K3zpUZcnf71TSICIiRSrfTxwqVqzIzz//nKd82rRpN6VDf7Vx40aHReV27txJly5deOCBB+xl3bp1Y/bs2fZtd3fH1VDHjRvHTz/9xJdffklgYCATJkygZ8+exMbG4uqqOc1FpOgYhuGw3bt3bwIDA0lISGD9+vVkZWXl+Z1lGAZPfbONmN1n7WXtqgfxxn0N2BuXTOOK/vj/d9XnTrVD6FQ7pOgvREREbnv5ThwgdzrA77//nj179mAymahduzZ9+vQpkg/h5cqVc9h+4403qFq1qsN6EhaLhdDQK/+lLSkpiVmzZvHZZ5/RuXNnAObNm0dERATLli2ja9euN73PInJ7s9lsLF68mPfee4+AgADuvvtue52npydvvfUWfn5+9OnTBzc3t//uY5ByKZvkS1Y++f0IMbvP4u7qwpi7quHv7c59jcvj5e6mwc4iIuI0+U4cDh48SI8ePTh16hQ1a9bEMAz2799PREQECxcupGrVqkXRTwCysrKYN28e48ePd1joaOXKlQQHB1O2bFnat2/Pq6++SnBwMACxsbFYrVaioqLs7cPDw6lXrx5r1669auKQmZlJZmamffvywG+r1YrVai2Ky7uqy+cr7vPeKhS/glPsCubEiRP06tULm82Gv78/aWlpeHt72+uHDBkC5D5ZsFqtXEjLYticWPacSXE4zvM9ajK4ecR/t4zb6t9B917hKH4Fp9gVjuJXcM6KXX7OZzL++hz9Onr06IFhGHz++ecEBAQAkJCQwIMPPoiLiwsLFy7MX2/z4euvv2bQoEEcP36c8PBwAL766ivKlClDZGQkR44c4cUXXyQ7O5vY2FgsFgtffPEFw4cPd0gCAKKioqhcuTIzZ8684rkmT57MlClT8pR/8cUXeHl53fyLE5FSKzMzE4vF4lD2xhtvsH79esqVK8ekSZOuOnmEzYCP9rqw5+KfQ86q+hi0CrHRNMjApCUYRESkCKWnpzNo0CCSkpLw9fW9Ztt8Jw7e3t6sX7+e+vXrO5Rv27aNNm3akJqamv8e36CuXbvi7u7OTz/9dNU2cXFxREZG8uWXX9K3b9+rJg5dunShatWqfPjhh1c8zpWeOERERHD+/PnrBvVms1qtxMTE0KVLF8xmTa+YX4pfwSl2V2ez2Vi4cCEffPAB6enprFq1yqF+y5YtHD16FDc3N7p165YnfhfTrUz+eQ9bT1zk1MVLWNxc+Gpkc2qGlMHNNd/zVtxydO8VjuJXcIpd4Sh+Bees2CUnJxMUFHRDiUO+X1WyWCykpKTkKU9NTc0zwO9mOnbsGMuWLWPBggXXbBcWFkZkZCQHDhwAIDQ0lKysLBITE/H397e3i4+Pp3Xr1lc9jsViyfMXRACz2ey0HwRnnvtWoPgVnGKXl2EYTJo0iZ07dwKwfft2mjRpYq9v3rw5jRo14pdffskTv0vWHB79YiuxxxIBcHMx8eq99bkjMrB4L6IU0L1XOIpfwSl2haP4FVxxxy4/58r3n7V69uzJqFGj2LBhA4ZhYBgG69ev59FHH6V37975PdwNmz17NsHBwQ6DDK8kISGBEydOEBYWBkCTJk0wm83ExMTY28TFxbFz585rJg4iIv/r9OnTDtsmk4mxY8cCULVqVRISEm7oOIZhMP7r3KTB18ON2cOasXbiXdzfROvgiIhIyZbvxOG9996jatWqtGrVCg8PDzw8PGjTpg3VqlXj3XffLYo+YrPZmD17NkOHDrXPQAK5Tzmeeuop1q1bx9GjR1m5ciW9evUiKCiIe++9FwA/Pz9GjBjBhAkT+PXXX9myZQsPPvgg9evXt8+yJCJyNb/88gsdO3akSpUqnDt3zqFu8ODB/Pzzz+zfv99hAoa/Srn058CzT34/yi87zmB2NfHxQ03pWCuYYB+PIuu/iIjIzZLvV5XKli3LDz/8wIEDB9izZw8AderUoVq1aje9c5ctW7aM48eP8/DDDzuUu7q6smPHDj799FMuXrxIWFgYHTt25KuvvsLHx8febtq0abi5udGvXz8yMjLo1KkTc+bM0RoOInJdy5cvZ+XKlQB8/PHHPP/88/Y6b2/vaz4FTcvMZu5+F55ct4IaIWUIL+vJmgPnAfi/u+vQoopeTRIRkdKjQOs4AFSvXt2eLJiKeNqPqKioPIsoQe586EuWLLnu/h4eHkRHR+dZpVVE5H9t3bqVevXqOTzZfOyxx5g6dSo1atSgYsWKN3QcwzBYue8cL/20iyMJuQ92959NZf/Z3Mkj7rkjnIdaRd78CxARESlCBUocZs2axbRp0+wDkKtXr864ceN45JFHbmrnRESKw2+//cbEiRP5/fff+c9//sN9991nr6tSpQqbNm3ijjvuwMXl+m93GobBs99u5+tNJwHwMxtMG9SElEwbKZeyqRPuS6OIskX+BxcREZGbLd+Jw4svvsi0adMYO3YsrVq1AmDdunX8/e9/5+jRo7zyyis3vZMiIkUpIyOD33//HYDo6GiHxAGgcePG1z3GJWsO51Iy+U/sSb7edBJXFxPDWlWkWtYh2lUL0uwiIiJS6uU7cZgxYwYff/wxAwcOtJf17t2bBg0aMHbsWCUOIlKibdy4kcDAQKpUqWIv69y5MzVr1sTV1ZUBAwZgGAYmk4k9ccmYXV2oFlzmqsfbcTKJ6OUHWH3gHJesNnv5S33q0q9xOL/8cqhIr0dERKS45DtxyMnJoWnTpnnKmzRpQnZ29k3plIjIzbZ//34eeughNmzYwMiRI/noo4+A3AHMsccS+du0r0jIcmX9hXS2f7GZpAwrvx9MwGSCB1tE8lTXmvh5/vnU4GB8CnPWHuWLDcex/XcIlsXNBbOrC4+0q8zgFpFYrdYrdUVERKRUynfi8OCDDzJjxgymTp3qUP7RRx8xePDgm9YxEZGbKSwsjN27d2MpX4f5i1Yz4dgZpq4+ya974sm25Z18AcDFBDYDPlt/jF/3nGVS77qU87Hw/vKD/Lo33t6ud8NwRrevQp0wX41dEBGRW1aBB0cvXbqUli1bArB+/XpOnDjBQw89xPjx4+3t/ppciIgUNcMwWLduHYmJiQ5TpVo8vWk88k2OmnNnRur50WasObkJQwV/T+qG+1IpyJtKgd5kZOWQnpVN74blOXkxnecX7OBoQjqjP4u1H8/VxUTHmsE83KYSrasFFe9FioiIOEG+E4edO3faBwoeOpT77m65cuUoV64cO3futLfTX91EpLhdunSJdu3asWnTJipVqkS7jp1Ztvccv+yIY8PhC6SYK2IygdnFhawcG/XL+/HmfQ2oE+571WNWDPRi4RPt+OeSfSzfG09iehatqgTybPdaVC139bEPIiIit5p8Jw4rVqwoin6IiBTa6ZRsUluMIqTG/SSdOUjL12JIz/7zjxhBZdz55/0NuSOiLLtOJ9OiSgBm1+tPseptcWNy77pM7l23KLsvIiJSohV4ATgREWcxDIPffvuNVatW8eKLL3LJmsOP207z8s+7ySgTjkeZcDwi6pGeDZUCvbinUXk61w6hdpgvri65iUTb6nq9SEREJD+UOIhIqXPffffx3fc/UK7Pc8x9fiEmk8k+XqFJpD9d6oSw63QynWsH07NBuD1ZEBERkYJT4iAipU67du1Ycb4MXjVbk20DMAj38+Ch1pUY3qYSFjdXZ3dRRETklqPEQURKJMMwWLFiBR999BEzZ87E19eXmN1n+dfSfRy/UAu/1jUAeO2eOrSrEUKYnwduNzBeQURERApGiYOIlEhTpkxhypQpALRq1YoLlToxd90xhzbD21RiUMvKzuieiIjIbUeJg4iUSA888IA9cZi79ggX4o5hMsGj7avSr2kEkDvwWURERIqHnuuLiNMYhsHSpUvp1asXS5YscairW7cu48ePZ/z0/5BcNQqAZ7rW4tlutagc5E3lIG+tFyMiIlKM9MRBRJxm0aJF9tWdc3Jy6Nq1K5CbUKw9lEDqHQNZsussYHB/kwo82r6KE3srIiJye1PiICLFxmaz4eLy54POqKgoIiMjOXbsGLt27SI1NZUyZcrwxuK9zFx1GACTCZ6KqsljHarqCYOIiIgTKXEQkSJls9lYunQp0dHR1KpVi7ffftte5+bmxltvvYWrqyt9+vTBzc2NGSsP2ZOGgc0rMqRlJHXCfZ3VfREREfkvJQ4iUqQSExO59957uXTpEmvWrGHKlCmUKVPGXt+vXz/79/P/OM6bi/cCMLF7LUa3r1rs/RUREZEr0+BoEbmp0tPTHbYDAwMZPHgwAP7+/hw4cMCh3jAMDMPg8w3HeP67HQD8rUNVJQ0iIiIljJ44iEihGYbBL7/8QnR0NKdOnWL79u0O4xGeeuopevbsSa9evUi32jh8LpW0zBxe+2UPW04kEl7Wk8Pn0oDc15Oe6VrTWZciIiIiV6HEQUQKzWQy8cYbb7BmzRoAli9fTqdOnez1bgHlMVXyYdJPu/lP7EkuWW0O+x8+l4abi4kJUTUZfWcVDYIWEREpgZQ4iEi+nTp1ivLlyzuUPfHEE6z5fS2RfZ9m0toMfjy3hXJlLOyPT2X1/nMObT3MLmRl2+hcO4S/dajKycQMaof5Ui24DCIiIlIylegxDpMnT8ZkMjl8hYaG2usNw2Dy5MmEh4fj6elJhw4d2LVrl8MxMjMzGTt2LEFBQXh7e9O7d29OnjxZ3JcicktYtmwZXbp0ITIykqNHjwKQmJbF9OUHOOhVl15v/ADV2nEyzcQPW0/z7zVHWL3/HC4maF4pgH5NK/DFyBbseakbB17twUcPNaVRRX96NQxX0iAiIlLClfgnDnXr1mXZsmX2bVdXV/v3b731FlOnTmXOnDnUqFGDV155hS5durBv3z58fHwAGDduHD/99BNffvklgYGBTJgwgZ49exIbG+twLBG5vvXr19t/Ht/74EOqdBvBzFWHScnM/m8LE2ZXE891r01Wto2L6VmYXV3o1zSCioFeDsdy1dtIIiIipUqJTxzc3NwcnjJcZhgG77zzDi+88AJ9+/YFYO7cuYSEhPDFF18wevRokpKSmDVrFp999hmdO3cGYN68eURERLBs2TL7KrUikteuXbuIiIhwKBs1ahQvv/wy5VvczRJza9KW7gegVqgPDSuU5fD5VB7rWI2ONYOd0WUREREpQiU+cThw4ADh4eFYLBZatGjBa6+9RpUqVThy5AhnzpwhKirK3tZisdC+fXvWrl3L6NGjiY2NxWq1OrQJDw+nXr16rF279pqJQ2ZmJpmZmfbt5ORkAKxWK1artQiu9Ooun6+4z3urUPzyJzY2lueff54VK1bwwQcfEB4ebo+dn19ZHopeRMzhDNJyIMLfk3GdqtGzfiguLn8+QlCsc+neKzjFrnAUv4JT7ApH8Ss4Z8UuP+czGYZhFGFfCmXRokWkp6dTo0YNzp49yyuvvMLevXvZtWsX+/bto02bNpw6dYrw8HD7PqNGjeLYsWMsWbKEL774guHDhzskAABRUVFUrlyZmTNnXvXckydPZsqUKXnKv/jiC7y8vK6wh8it4cCBAzz99NMAVKpUiWnTpmFgIsUKMSdd+O2sCyYMOpU36F7BhluJHiklIiIi15Kens6gQYNISkrC19f3mm1L9BOH7t2727+vX78+rVq1omrVqsydO5eWLVsC5Jm20TCM607leCNtJk6cyPjx4+3bycnJREREEBUVdd2g3mxWq5WYmBi6dOmC2Wwu1nPfChS/q9u+fTtms5natWs7lP/nP/8hISGB0aNHk3jJxhenAzgQn7vOgskE/7qvAb0bhjmjy6WK7r2CU+wKR/ErOMWucBS/gnNW7C6/VXMjSnTi8Ffe3t7Ur1+fAwcOcM899wBw5swZwsL+/AATHx9PSEgIAKGhoWRlZZGYmIi/v79Dm9atW1/zXBaLBYvFkqfcbDY77QfBmee+FSh+fzpx4gRDhgxh1apVPPDAA3z99dcO9T/88APlypUjMfUSPd9ZTlx6Gi4mKOdjYUJUTe5rGnGVI8uV6N4rOMWucBS/glPsCkfxK7jijl1+zlWqXjLIzMxkz549hIWFUblyZUJDQ4mJibHXZ2VlsWrVKntS0KRJE8xms0ObuLg4du7ced3EQeRWFhwczN69ewFYsGABJ06ccKgPCQnBwMSTX28nLt1EuTLurHq6Ixue70w/JQ0iIiK3pRKdODz11FOsWrWKI0eOsGHDBu6//36Sk5MZOnQoJpOJcePG8dprr/Hdd9+xc+dOhg0bhpeXF4MGDQLAz8+PESNGMGHCBH799Ve2bNnCgw8+SP369e2zLInc6rZu3cr333/vUGaxWBg9ejQ1a9bk3XffdXgid9k7y/az5mAC7i4G/36oMREBGtsjIiJyOyvRryqdPHmSgQMHcv78ecqVK0fLli1Zv349kZGRADzzzDNkZGTw2GOPkZiYSIsWLVi6dKl9DQeAadOm4ebmRr9+/cjIyKBTp07MmTNHazjILS8nJ4eoqCiWL19OuXLl6NatG2Z3C67/nf1o4sSJTJo0CReXvH8/+GnbaaKXHwSgfxUbdcKKd1yPiIiIlDwlOnH48ssvr1lvMpmYPHkykydPvmobDw8PoqOjiY6Ovsm9EynZXF1dCQ7OXU/hImW4f+ov7E/zpFXVQJ7vUZsMaw5Vyrni6+GYOKzYF8+Er7cBMLx1JHcYh4q97yIiIlLylOjEQUSu7UzSJT5cdYg9x+I4HhdPWIVIOtUOYfSdVXBzdWHs2LFs2X8MW9REdia7ADZW7T/Hqv3nAPDzNPPOgDuoG+7LxiOJfLXpBKv/W9e9XijPdq3BksVKHERERESJg0ipdTE9iwdnbeBgfOp/S/yIO36Rzccv8vP2OOqE+VIjJIQmj07l90MJNKjgx98712Dm6kNsOHKBMu5uJGVYGT57o8NxXV1M9G8WwT961sEVW/FfmIiIiJRIShxESgHDMIhPySTlkpXZvx/l1z3xZFhzSMqw4uOWw9FfZmJkptO6Q2fiyjVlT1wye+L+nJfZ4ubCO/3voEq5MnSsFYw1x4bNMJj8426+2ngcA4gM8KJrvVAGNqtIpSBvAKxWJQ4iIiKSS4mDSAm1cl886Vk5dKhZjpGfbuL3gwl52pT1MvPp0BY8+fs0Bg4cyODBg0nJdmXZnrNcTM9ixb5zbD6eyIs961ClXBn7fmbX3HENr/etz6RedTC7utgHTYuIiIhciRIHkRLi1MUMHp69kQr+nnSoFcyL3+8EIKiMhfOpmRiGDXJyCHfP4I1hnSljcaNGSBl8PMysWLHCfhxv4MGWuTOPjbmrOjk245pJgYdZM4yJiIjI9SlxECkBsrJtjPliM/vOprDvbAq/7o23151PzcTd1cTJzyaScWIXPnXrcuerAzCZbuwJgZ4kiIiIyM2gxEHEiVIzs/nn4r1sOHKBvWdS8DKbsKUnc8nsQ9e6IYzpWJ1Pfj/CA00q8JOtF9Wq/Z2BAwfecNIgIiIicrMocRBxoo9XH2buumMAuJrg6Jcvcen4Dhp2vpfoVz7F3c2Faf3vAKD16687saciIiJyu8u7ZKyIFItLWdnMW5+bNPy9cw1WPt2Bap7pGFnpnNiwmAvn469zBBEREZHioycOIsVs/fr1vPvuuyQH1iWhTCPC/Tx4vGNV3FxdePnll7lw4QIDBgzA09PT2V0VERERsVPiIFKM0tPT6d69OxeTUwgffifmMvBQ60q4/Xd61D59+ji5hyIiIiJXpleVRIqQ1Wp12Pby8mLEiBH4teqHOagiXm4woFmEk3onIiIicuOUOIgUgdjYWB566CHq1KlDdna2vTwxLYsKHQcR0HYQAK/ffwdlvdyd1U0RERGRG6ZXlUSKwOTJk/n5558B+O6773jggQeIS8qgV/QazqdmASbubhBG74bhzu2oiIiIyA3SEweRQkpOTs5T9uSTTwLg7+/PxYsXAXj9l72cT80iIsCT53vU4u0HGmo9BhERESk1lDiIFNCuXbt45JFHCAkJYfv27Q51nTp14vPPP+fkyZOMHDmSjUcv8OO205hMMGNwE0bdWRUPs6uTei4iIiKSf0ocRApo5cqVzJo1i0uXLhEdHe1QZzKZGDRoEF5eXiSlW3nmP7mJRf+mEdQr7+eM7oqIiIgUihIHkRuQmJhISkqKQ9lDDz2Er68vvr6+BAcHX3G/tMxsxszfzJHzaZQv68kz3WoVR3dFREREbjolDiLXcPz4cR599FEqVKjAzJkzHep8fHxYuHAhp06d4tVXX3Wos+bY+GzdUdr/cyW/HTiPp9mVjx5qQoC3ZlASERGR0kmzKolcQ0ZGhj1hmD59On//+99xdf1zbELbtm3t3+fYDH7cdooNhy+w9lACxy+kAxAZ6MVr99anbrheURIREZHSS4mDyH8lJSVx/vx5qlatai+rWbMmXXr1ZeO+E7Tu3oOLySkE+pfNs++GwwlM+Wk3u+P+nGEpqIw7T3SqzoBmFXF308M9ERERKd2UOMhtLzU1lYkTJzJnzhxatmxJTEyMvW7prjMcqTcCvzoGa4E+H23m7gZhmDBx4kI6ielZ2AyD9YcvAODr4cagFpHUDfflrlrBeFv0IyYiIiK3Bn2qkduel5cXixYtIjX9EpvdatNo8mLSsg1qhJRh/5lUrDaD8mU9Sc/K5mRiBjNXHc5zDJMJBjavyIQuNQgsY3HCVYiIiIgUrRKdOLz++ussWLCAvXv34unpSevWrXnzzTepWbOmvc2wYcOYO3euw34tWrRg/fr19u3MzEyeeuop5s+fT0ZGBp06deKDDz6gQoUKxXYtUjKkpKSwZcsW7rzzTnuZi4sLjz0+hn+uOY+leisSL+UAsPNU7mtH3euFEj2wEdYcg/9sPsmh+FRMJihf1pOgMhbSsrJpGhlAzVAfp1yTiIiISHEo0YnDqlWrePzxx2nWrBnZ2dm88MILREVFsXv3bry9ve3tunXrxuzZs+3b7u6OM9eMGzeOn376iS+//JLAwEAmTJhAz549iY2NdRjoKre2SZMm8f77H2Cz2Th58gR+frmDlW02g6MhbbFUP4u7qwtT+zekbrgfsccSSc6w8mDLSNxcXXBzhSEtI518FSIiIiLOUaITh8WLFztsz549m+DgYGJjYx3+YmyxWAgNDb3iMZKSkpg1axafffYZnTt3BmDevHlERESwbNkyunbtWnQXICXKmYQkvHq/iFtgBf4W/T01GjRlT1wyJhOsP3wBVxcT0YMa0bVu7r1UOcj7OkcUERERuX2U6MThr5KSkgAICAhwKF+5ciXBwcGULVuW9u3b8+qrr9oX5IqNjcVqtRIVFWVvHx4eTr169Vi7du1VE4fMzEwyMzPt28nJua+tWK1WrFbrTb2u67l8vuI+b2mVnp7OggULGDRoEC4uLmRlZZFwCc7W6IPlXG4M16aWYe3ao/Z9TCZ4s2897qoRqDj/D917haP4FZxiVziKX8EpdoWj+BWcs2KXn/OZDMMwirAvN41hGPTp04fExER+++03e/lXX31FmTJliIyM5MiRI7z44otkZ2cTGxuLxWLhiy++YPjw4Q5JAEBUVBSVK1fOs6jXZZMnT2bKlCl5yr/44gu8vLxu7sXJTRMTE8PcuXNJTU3lxRdfpFaDJszc68qxVBMAFheDLhVs7LjgQll3gzr+BomZEFEG6vmXih8FERERkZsmPT2dQYMGkZSUhK+v7zXblponDmPGjGH79u2sWbPGobx///727+vVq0fTpk2JjIxk4cKF9O3b96rHMwwDk8l01fqJEycyfvx4+3ZycjIRERFERUVdN6g3m9VqJSYmhi5dumA2m4v13KWN1Wrlg48/wa/dgyw5mMqxyFCOpZ7HxWRQP9yPid1r0iTS39ndLDV07xWO4ldwil3hKH4Fp9gVjuJXcM6K3eW3am5EqUgcxo4dy48//sjq1auvOxNSWFgYkZGRHDhwAIDQ0FCysrJITEzE3//PD4zx8fG0bt36qsexWCxYLHmn1TSbzU77QXDmuUuaS5cuMX/+fNq3b0+VKlXs5XdG3U3ksKkY/hGcBc4eOI/FzYUn6mQx6oGWil8B6d4rHMWv4BS7wlH8Ck6xKxzFr+CKO3b5OVeJXs7WMAzGjBnDggULWL58OZUrV77uPgkJCZw4cYKwsDAAmjRpgtlsdljUKy4ujp07d14zcZCSa/Xq1URERPDwww/z3nvvAXAuJZO3l+4j6p3fMPwj8PcyUzHAC1cXE6/eU5cKGucsIiIiUigl+onD448/zhdffMEPP/yAj48PZ86cAcDPzw9PT09SU1OZPHky9913H2FhYRw9epTnn3+eoKAg7r33XnvbESNGMGHCBAIDAwkICOCpp56ifv369lmWpHSpV68eaWlpAHwy9zPK3DmMrzfHkZVtA6BKOW8+fqgplQO9ScnMxssNfjm1xZldFhERESn1SnTiMGPGDAA6dOjgUD579myGDRuGq6srO3bs4NNPP+XixYuEhYXRsWNHvvrqK3x8/lyMa9q0abi5udGvXz/7AnBz5szRGg4lXGZmJl9//TU+Pj7cc8899vKAgACGDx/O2ZRMLtZ9gHl/nALgjoiyjL6zClF1Q3F1yR2/4udp1swOIiIipUx8fHyeiW1udTabjYiICE6fPo2Ly819KchisdhnHC2MEp04XG/CJ09PT5YsWXLd43h4eBAdHU10dPTN6poUsfPnz1OvXj3Onj1L7dq16dOnj8Ng9r9PeoOhn2zkVGIGZb3MTOt3Bx1qlrvmgHcREREp+ZKTkzGZTERERDi7K8XKZrPh5+eHr6/vTU8czp07R3JycqEn+CnRYxzk9hUUFESNGjUA2LNnj302rczsHOauPcoDH67j1MUMqgR58+PjbelYK1hJg4iIyC0gKSmJoKAgZ3fjlhIUFGRfD60wSvQTB7n1Wa1Wvv32W3bu3Mkrr7wC5D5pWn3gPHc/PIGg8Ip06T8CI6QmxxLS+Nu8zeyOy502rH55P2YPb0ZQmbyzX4mIiEjppT8G3lw3K55KHMSp2rZtyx9//IGLiwsjRoygfEQkk37cyfw/TgBuUGkgmzekw4aN9n0Cvd0Z16UG/ZtG4O6mh2YiIiIixUGJgzhV7969+eOPPzBc3Xn+01854VGFk4kZmEwQVMbCuZRMwvw8sOYYnE/NpE6YLx8PbUr5sp7O7rqIiIjIbUWJgxS57Oxsvv/+e+bMmcPXX3+Nl5eXvW7UqFEsO5hMQsSdrMsAMjII8Hbn7Qca0qFmORLTrfh7mcmxGew9k0L1kDJY3DQbloiIiNy+jh49SuXKldmyZQt33HFHsZ1XiYMUufHjx9tntPps3uc06NSXDUcS8PUwk5lt40jInZAFkYFePNahKn3uKI+HOTc5CPB2B8DN1US98n5OuwYRERGRK7ne+IGhQ4cyZ86c4ulMEVPiIEVuyJAhREdH4+oTyHu73Eg7vD5Pm9F3VuGprjUxu2rMgoiIiJQecXFx9u+/+uor/vGPf7Bv3z57maen4+vVVqsVs9lcbP27mfQpTW6KnJwcfvzxRzp37sxvv/1mL8/OsXHAFkKLZz6l2ti5pHkG42Nxo3fDcBpVLAvA4x2r8lz3WkoaREREpNQJDQ21f/n5+WEymezbly5domzZsnz99dd06NABDw8P5s2bR0JCAgMHDqRChQp4eXlRv3595s+f73Bcm83Gm2++SbVq1bBYLFSsWJFXX331in2w2WyMHDmSGjVqcOzYsSK7Vj1xkJtiwYIF9OvXD4CyZcvSrl071h9OYPKPu9h7JgVMAZADdcN9mTG4CRUDc8c5XLLm2F9LEhEREbmSqVOnMnXqVADmzZtHhw4d7HVHjhyhXbt2ANx77715Fvzt3bs3mzdvBuDkyZMOdXPmzOH//u//AHjvvffo27dvkfT/2Wef5e2332b27NlYLBYuXbpEkyZNePbZZ/H19WXhwoUMHTqUxYsXc9dddwEwceJEPv74Y6ZNm0bbtm2Ji4tj7969eY6dlZXFoEGDOHToEGvWrLkpK0RfjRIHKRDDMBze6evTpw+hoaGcOXOGHYdO8ti8Tfyy8ywAfp5m/tahKi2rBFK/vB+uLn/up6RBREREric5OZlTp04BkJmZ6VCXk5Njr0tMTMyz77lz5+z1f5WWlmavS09Pv5lddjBu3Lg8SclTTz1l/37s2LEsWrSIH374gbvuuouUlBTeffddpk+fztChQwGoWrUqbdu2dThGamoqd999NxkZGaxcuRI/v6IdD6rEQW6YzWZj8eLFvPfeezRr1oyXX37ZXufmZmbgC9EcveTJniRXftl5FhcTDGpRkQldauL/30HOIiIiIvnl6+tL+fLlAbBYHBd+dXV1tdf5+/vn2bdcuXL2+r/y9va21/3vrI83W9OmTR22c3JyeOONN/jqq684deoUmZmZZGZm2q9tz549ZGZm0qlTp2se9/LrTr/++muR9v8yJQ5yw86ePUufPn3Izs4mNjaWF154AQ8PD7KybTz1zTZ+PHl58E8OzSsFMKl3HeqGayYkERERKZzx48czfvz4K9ZVrlw5zytI/+vHH3+8at2wYcMYNmxYYbt3Xd7e3g7bb7/9NtOmTeOdd96hfv36eHt78+STT5KVlQXkHVB9NT169GDevHmsX7/e/opTUVLiIFf1v5kvQFhYGA888ADz58/Hx8eHvfsPcpIAZqw8xK7Tybi5mHisQ1Xa1ShH00h/LRcvIiIicgW//fYbffr04cEHHwRy3+o4ePAg1apVA6B69ep4enry66+/8sgjj1z1OH/729+oV68evXv3ZuHChbRv375I+63EQRwYhsGyZct47733iI+PZ/369Q4JwMSJE2nfqz8nPKow9LvTJGXkjtz3dnfl/cGN6VCz6AbkiIiIiNwKqlWrxrfffsvatWvx9/dn6tSpnDlzxp44eHh48Oyzz/LMM8/g7u5OmzZtOHfuHLt27WLEiBEOxxo7diw5OTn07NmTRYsW5RkHcTMpcZA8nn32WbZs2QLAunXraN26NYZhsHLfOT75I53fDrgBxwEI9rEwoHlFhraKJLCM5RpHFRERERGAF198kSNHjtC1a1e8vLwYNWoUffr0ISEhwaGNm5sb//jHPzh9+jRhYWE8+uijVzzeuHHjsNls9OjRg8WLF9O6desi6bcSh9vchQsXCAgIsG+bTCaefPJJhg0bRkREBOfPn2fnqSTeWLSXNQfPA+Bigi51QhjSshKtqgY6zJIkIiIicrv665iJSpUqYRhGnnYBAQF8//33DmU2m43k5GT7touLCy+88AIvvPBCnv2vdNxrjQO5WZQ43KZ+//133n77bRYtWsThw4cJCwuz1/Xv3x8PrzK4V2nO3D9OELt2DQDubi481DKSoa0rERFQ9CP3RURERKTkUOJwm1q4cCHfffcdADNnzmTy5MkA2GwGS/Ym8N4hf07FbgfAzcXE3Q3CmNClpn3hNhERERG5vShxuA2cOHGCkJAQ3N3/XEvhb3/7G2+99RYhISGUK1cOgE1HL/Dyz7vZdjIJgHI+Fh5sEcnA5hEE+3o4pe8iIiIiUjIocbiF7dy5k5deeokFCxbw2WefMXDgQHtdREQEK1eupEWLFlgNE5N/3MWctUeB3BmSHutYjRFtK2tlZxEREREBlDjc0s6fP88333wDwLvvvuuQOAC0at2Gb2NP8nbMPs4m5y7f3r9pBE91rUk5H82QJCIiIiJ/UuJwi4iLi8NqtVKxYkV7Wfv27WnQoAFnzpyhW7duZGdn4+bmlju16v5zvPHLXvadTQGgfFlPXutbn/Y1yjnrEkRERESkBFPiUMqdOXOGCRMm8PXXXzN48GDmzJljrzOZTHz77bdERETYV4DeE5fMKwt38/vB3HmCfT3cGHtXdYa0itRrSSIiIiJyVS7O7kBx+uCDD6hcuTIeHh40adKE3377zdldKjQfHx8WLVpEdnY28+fP5+zZsw711apVw2KxkJRhZfKPu+gZvYbfDybg7urCqDursPqZjoy8s4qSBhERERG5ptsmcfjqq68YN24cL7zwAlu2bKFdu3Z0796d48ePO7trNyw+Pp7ff//doczb25tHHnmEwMBAnnrqKVxdHRMAm83g600nuOtfK5mz9ig5NoMe9UP5dUJ7nu9Rm7Je7oiIiIiIXM9tkzhMnTqVESNG8Mgjj1C7dm3eeecdIiIimDFjhrO7dl02m43o6GiqVKnCgAEDsFqtDvXPP/88J06c4NVXXyUoKMhevv3kRfrOWMsz/9lOQloWVct5M29ECz4Y3EQLuImIiIgUsQ4dOjBu3Dj7dqVKlXjnnXec1p/Cui0Sh6ysLGJjY4mKinIoj4qKYu3atU7q1Y1zcXEhJSWFrKwsTp48mWeJ8rJly+Lp6WnfTr5k5f++30Gf939n64mLeLu78nyPWix68k7aVg9CRERERG6eYcOGYTKZ8ny99dZbvPzyy1fdz2Qy5flcV5LdFoOjz58/T05ODiEhIQ7lISEhnDlz5or7ZGZmkpmZad9OTk4GwGq15vmLf1GzWq3cfffd7N+/n4cffpjGjRtftQ9Ld5/lpZ/3cjYlt++9G4TxTNfqhPh6gJGD1ZpTnF0vES7Hqrj/3W4Fil3hKH4Fp9gVjuJXcIpd4dyM+NlsNmw2283qUrEwDIOuXbvyySefOJSXK1cOV1dXh+sxDMNh+/L1GoZxxfobYbVaMZvN12xjs9mu+O+Sn3+r2yJxuMxkMjlsG4aRp+yy119/nSlTpuQpX7p0KV5exf+aT4MGDZg5cyYWi4WdO3eyc+dOh/qLmfCfIy7sSMx9iFTOw6B/FRvVvU8Qu+ZEsfe3JIqJiXF2F0otxa5wFL+CU+wKR/ErOMWucAoTv4iICPz8/IDcz2qXrM5JIjzMLlf9nPhXVqsVV1fXPJ8RO3bsSP369Xn99deB3A/vly5dIjk5mQYNGgBw3333AbnXvX37dlJSUli0aBFvvvkme/fuJTQ0lIEDBzJhwgTc3HI/uvv7+/P222+zbNkyVq1axZgxY5g4ceI1+5iQkMDWrVvzlKenp9/QNcJtkjgEBQXh6uqa5+lCfHx8nqcQl02cOJHx48fbt5OTk4mIiCAqKgpfX98i7e9fWa1WYmJi6NmzZ55s0mYzmL/pJP9aeoDUzGzcXEyMbFuJxzpopqTLLsevS5cu183GxZFiVziKX8EpdoWj+BWcYlc4NyN+p0+ftn/WSs/KptGbzknidk7ugpf7jX1UNpvNuLm55fmM6Obmhru7u73cxcUFDw8PfH192bhxI6GhocyaNYtu3brh4pL7x9+1a9fy6KOP8s4779CuXTsOHTrEo48+isVi4R//+If92G+++Savvvoq7733Hq6urtf9fBoYGEj9+vXzlF9+q+ZG3BaJg7u7O02aNCEmJoZ7773XXh4TE0OfPn2uuI/FYrGvffC/zGaz036R/PXcxxLSmPD1NjYdSwTgjoiyvHFffWqFFm9iU1o489+utFPsCkfxKzjFrnAUv4JT7AqnMPFzcXGxf4i+/F9n+N9+XI/JZGLhwoUOH967d+9ur/vf41zevvzH64CAAMLDw7HZbCQnJ/PGG2/w3HPPMXz4cCB3av2XX36ZZ555hsmTJ9uPM2jQIB555JF8Xc+V/k3y8+90WyQOAOPHj2fIkCE0bdqUVq1a8dFHH3H8+HEeffRRZ3ct3wzD4NvNp5j0w07SsnLwdnfl6a41GdKqEq4uN/ZITURERKSk8zS7svulrk47d3507NjRYbZOb29vBg4cmO/zxsbGsnHjRl599VV7WU5ODpcuXSI9Pd3+OlTTpk3zfezCum0Sh/79+5OQkMBLL71EXFwc9erV45dffiEyMtLZXcuXlEtWnluwg4Xb4wBoXimAqf0bUsFf06uKiIjIrcVkMt3w60LO5u3tTbVq1Qp9HJvNxpQpU+jbt2+eOg8PD4fzFbfS8S9xkzz22GM89thjzu5GgZ1ITOfRz7ey/2wqbi4m/t6lBo+2r6qnDCIiIiKlkNlsJifHccbLxo0bs2/fvpuShNxst1XiUJpdzISBH2/kbEomIb4WPnywCY0q+ju7WyIiIiJSQJUqVeLXX3+lTZs2mM1mXF1d+b//+z969+5NREQEDzzwAC4uLmzfvp0dO3bwyiuvOLW/t8UCcKVdWmY2H+115WxKJtWDy/DD422VNIiIiIiUcm+//TYxMTFERETQpEkTALp27crPP/9MTEwMzZo1o2XLlkydOrVEvF6vJw6lwLMLdnIq3USgtzufDGtGqJ/H9XcSERERkWIxZ86cK5avXLnSYfvo0aMO27169aJXr14A9lmVIDd56Nr16oPCLy8WV9z0xKEU6N+sAj5mgxmD7iAiQIOgRURERKT4KXEoBdpVC+IfjXJoVLGss7siIiIiIrcpJQ6lhLsWgRYRERERJ1LiICIiIiIi16XEQURERERErkuJg4iIiIiUKM6aNehWdbPiqcRBREREREoMPz8/zp8/7+xu3FLOnz+Pn59foY+jdRxEREREpMTw9fUlPj6eEydOOLsrxcpms5GQkEBgYCAuLjf3b/sWiwVfX99CH0eJg4iIiIiUKMHBwc7uQrGzWq1s3bqV+vXrYzabnd2dK9KrSiIiIiIicl1KHERERERE5LqUOIiIiIiIyHUpcRARERERkevS4OgbdHn+2+Tk5GI/t9VqJT09neTk5BI7WKYkU/wKTrErHMWv4BS7wlH8Ck6xKxzFr+CcFbvLn21vZK0HJQ43KCUlBYCIiAgn90RERERE5OZKSUm57loPJkNL890Qm83G6dOn8fHxwWQyFeu5k5OTiYiI4MSJEzdlDt7bjeJXcIpd4Sh+BafYFY7iV3CKXeEofgXnrNgZhkFKSgrh4eHXXT9CTxxukIuLCxUqVHBqH3x9ffVDWAiKX8EpdoWj+BWcYlc4il/BKXaFo/gVnDNid6OrSmtwtIiIiIiIXJcSBxERERERuS4lDqWAxWJh0qRJWCwWZ3elVFL8Ck6xKxzFr+AUu8JR/ApOsSscxa/gSkPsNDhaRERERESuS08cRERERETkupQ4iIiIiIjIdSlxEBERERGR61LiICIiIiIi16XEoYT44IMPqFy5Mh4eHjRp0oTffvvtmu1XrVpFkyZN8PDwoEqVKnz44YfF1NOS5fXXX6dZs2b4+PgQHBzMPffcw759+665z8qVKzGZTHm+9u7dW0y9LhkmT56cJwahoaHX3Ef33Z8qVap0xfvo8ccfv2L72/m+W716Nb169SI8PByTycT333/vUG8YBpMnTyY8PBxPT086dOjArl27rnvcb7/9ljp16mCxWKhTpw7fffddEV2Bc10rflarlWeffZb69evj7e1NeHg4Dz30EKdPn77mMefMmXPF+/HSpUtFfDXF63r33rBhw/LEoGXLltc9ru69XFe6h0wmE//85z+veszb5d67kc8npfF3nxKHEuCrr75i3LhxvPDCC2zZsoV27drRvXt3jh8/fsX2R44coUePHrRr144tW7bw/PPP88QTT/Dtt98Wc8+db9WqVTz++OOsX7+emJgYsrOziYqKIi0t7br77tu3j7i4OPtX9erVi6HHJUvdunUdYrBjx46rttV952jjxo0OsYuJiQHggQceuOZ+t+N9l5aWRsOGDZk+ffoV69966y2mTp3K9OnT2bhxI6GhoXTp0oWUlJSrHnPdunX079+fIUOGsG3bNoYMGUK/fv3YsGFDUV2G01wrfunp6WzevJkXX3yRzZs3s2DBAvbv30/v3r2ve1xfX1+HezEuLg4PD4+iuASnud69B9CtWzeHGPzyyy/XPKbuvT/99f755JNPMJlM3Hfffdc87u1w793I55NS+bvPEKdr3ry58eijjzqU1apVy3juueeu2P6ZZ54xatWq5VA2evRoo2XLlkXWx9IiPj7eAIxVq1Zdtc2KFSsMwEhMTCy+jpVAkyZNMho2bHjD7XXfXduTTz5pVK1a1bDZbFes132XCzC+++47+7bNZjNCQ0ONN954w1526dIlw8/Pz/jwww+vepx+/foZ3bp1cyjr2rWrMWDAgJve55Lkr/G7kj/++MMAjGPHjl21zezZsw0/P7+b27kS7kqxGzp0qNGnT598HUf33tX16dPHuOuuu67Z5na89wwj7+eT0vq7T08cnCwrK4vY2FiioqIcyqOioli7du0V91m3bl2e9l27dmXTpk1YrdYi62tpkJSUBEBAQMB12zZq1IiwsDA6derEihUrirprJdKBAwcIDw+ncuXKDBgwgMOHD1+1re67q8vKymLevHk8/PDDmEyma7bVfefoyJEjnDlzxuHeslgstG/f/qq/A+Hq9+O19rldJCUlYTKZKFu27DXbpaamEhkZSYUKFejZsydbtmwpng6WMCtXriQ4OJgaNWowcuRI4uPjr9le996VnT17loULFzJixIjrtr0d772/fj4prb/7lDg42fnz58nJySEkJMShPCQkhDNnzlxxnzNnzlyxfXZ2NufPny+yvpZ0hmEwfvx42rZtS7169a7aLiwsjI8++ohvv/2WBQsWULNmTTp16sTq1auLsbfO16JFCz799FOWLFnCxx9/zJkzZ2jdujUJCQlXbK/77uq+//57Ll68yLBhw67aRvfdlV3+PZef34GX98vvPreDS5cu8dxzzzFo0CB8fX2v2q5WrVrMmTOHH3/8kfnz5+Ph4UGbNm04cOBAMfbW+bp3787nn3/O8uXLefvtt9m4cSN33XUXmZmZV91H996VzZ07Fx8fH/r27XvNdrfjvXelzyel9XefW7GcRa7rr3+lNAzjmn+5vFL7K5XfTsaMGcP27dtZs2bNNdvVrFmTmjVr2rdbtWrFiRMn+Ne//sWdd95Z1N0sMbp3727/vn79+rRq1YqqVasyd+5cxo8ff8V9dN9d2axZs+jevTvh4eFXbaP77try+zuwoPvcyqxWKwMGDMBms/HBBx9cs23Lli0dBgG3adOGxo0bEx0dzXvvvVfUXS0x+vfvb/++Xr16NG3alMjISBYuXHjND8C69/L65JNPGDx48HXHKtyO9961Pp+Utt99euLgZEFBQbi6uubJFOPj4/NklJeFhoZesb2bmxuBgYFF1teSbOzYsfz444+sWLGCChUq5Hv/li1b3tJ/7bgR3t7e1K9f/6px0H13ZceOHWPZsmU88sgj+d5X9x32mbzy8zvw8n753edWZrVa6devH0eOHCEmJuaaTxuuxMXFhWbNmt3292NYWBiRkZHXjIPuvbx+++039u3bV6Dfg7f6vXe1zyel9XefEgcnc3d3p0mTJvYZWS6LiYmhdevWV9ynVatWedovXbqUpk2bYjabi6yvJZFhGIwZM4YFCxawfPlyKleuXKDjbNmyhbCwsJvcu9IlMzOTPXv2XDUOuu+ubPbs2QQHB3P33Xfne1/dd1C5cmVCQ0Md7q2srCxWrVp11d+BcPX78Vr73KouJw0HDhxg2bJlBUrkDcNg69att/39mJCQwIkTJ64ZB917ec2aNYsmTZrQsGHDfO97q9571/t8Ump/9xXLEGy5pi+//NIwm83GrFmzjN27dxvjxo0zvL29jaNHjxqGYRjPPfecMWTIEHv7w4cPG15eXsbf//53Y/fu3casWbMMs9ls/Oc//3HWJTjN3/72N8PPz89YuXKlERcXZ/9KT0+3t/lr/KZNm2Z89913xv79+42dO3cazz33nAEY3377rTMuwWkmTJhgrFy50jh8+LCxfv16o2fPnoaPj4/uu3zIyckxKlasaDz77LN56nTf/SklJcXYsmWLsWXLFgMwpk6damzZssU+688bb7xh+Pn5GQsWLDB27NhhDBw40AgLCzOSk5PtxxgyZIjDTHO///674erqarzxxhvGnj17jDfeeMNwc3Mz1q9fX+zXV9SuFT+r1Wr07t3bqFChgrF161aH34OZmZn2Y/w1fpMnTzYWL15sHDp0yNiyZYsxfPhww83NzdiwYYMzLrHIXCt2KSkpxoQJE4y1a9caR44cMVasWGG0atXKKF++vO69/7rez65hGEZSUpLh5eVlzJgx44rHuF3vvRv5fFIaf/cpcSgh3n//fSMyMtJwd3c3Gjdu7DCd6NChQ4327ds7tF+5cqXRqFEjw93d3ahUqdJVf2BvdcAVv2bPnm1v89f4vfnmm0bVqlUNDw8Pw9/f32jbtq2xcOHC4u+8k/Xv398ICwszzGazER4ebvTt29fYtWuXvV733fUtWbLEAIx9+/blqdN996fLU9H+9Wvo0KGGYeROSzhp0iQjNDTUsFgsxp133mns2LHD4Rjt27e3t7/sm2++MWrWrGmYzWajVq1at2wSdq34HTly5Kq/B1esWGE/xl/jN27cOKNixYqGu7u7Ua5cOSMqKspYu3Zt8V9cEbtW7NLT042oqCijXLlyhtlsNipWrGgMHTrUOH78uMMxdO9d/WfXMAxj5syZhqenp3Hx4sUrHuN2vfdu5PNJafzdZzKM/45uFBERERERuQqNcRARERERketS4iAiIiIiItelxEFERERERK5LiYOIiIiIiFyXEgcREREREbkuJQ4iIiIiInJdShxEREREROS6lDiIiIiIiMh1KXEQEZHrWrlyJSaTiYsXLzrl/MuXL6dWrVrYbLYiP9eOHTuoUKECaWlpRX4uEZHSRImDiIg46NChA+PGjXMoa926NXFxcfj5+TmlT8888wwvvPACLi5F/7+t+vXr07x5c6ZNm1bk5xIRKU2UOIiIyHW5u7sTGhqKyWQq9nOvXbuWAwcO8MADDxTbOYcPH86MGTPIyckptnOKiJR0Shz+v737C2mybeA4/h17WrnsHxVWZo5q04QKK4gIE0FcnQTKLNJYf0iCUqGyFUhUJ0F0pCdWEBYSLomIKBM6aCstZC3KyogZm6OQJIsOUla0vQcv3bx7Mve8PfX8qd/nbNd9/buvo/12X/c1ERExbN26Fb/fT0NDAyaTCZPJRCQS+WKr0tmzZ5k6dSpXr14lJycHq9WKy+Xi/fv3nDt3DpvNxrRp06ipqUn68v3hwwc8Hg+ZmZlMnDiRlStX4vP5xpyT1+ulpKSECRMmGGUPHz6kqKiISZMmMXnyZJYvX869e/eM63fu3GHNmjWkpaWRlZVFbW1t0tajWCyGx+MhKyuL8ePHY7fbOXPmjHHd6XQyNDSE3+//kysqIvLzUHAQERFDQ0MDq1atoqqqioGBAQYGBsjKyhq17vDwMI2NjXi9Xjo6OvD5fJSVldHe3k57ezstLS2cPn2aixcvGm22bdtGV1cXXq+Xnp4eysvLWbt2LaFQ6KtzunXrFitWrEgqq6ysZO7cuQQCAYLBIAcPHmTcuHHAf99RcDqdlJWV0dPTw4ULF+js7KS6utpo73a78Xq9NDY28vTpU06ePEl6erpx3WKxsHTpUm7fvv1N6ygi8jP67e+egIiI/HNMmTIFi8WC1Wpl1qxZY9b9+PEjTU1NLFiwAACXy0VLSwuvXr0iPT2dvLw8ioqKuHnzJhs3buT58+e0trby4sUL5syZA0BdXR0dHR00Nzdz7NixUceJRCJG/c+i0Sj79+8nNzcXALvdblw7ceIEFRUVxnsadrudxsZGCgsLaWpqIhqN0tbWxo0bNyguLgZg/vz5X4ybmZlJJBJJvWgiIr8IBQcREfkmVqvVCA0AGRkZ2Gy2pF/uMzIyGBwcBOD+/fskEgkcDkdSP7FYjOnTp391nJGRkaRtSgB79+5lx44dtLS0UFxcTHl5uTGXYDBIX18f58+fN+onEgni8TjhcJhHjx5hNpspLCwc8/7S0tIYHh5OsQoiIr8OBQcREfkmn7cGfWYymUYt+3yEajwex2w2EwwGMZvNSfX+N2z83owZM3j79m1S2ZEjR6ioqODatWtcv36dw4cP4/V6KS0tJR6Ps3PnTmpra7/oa968efT19f2h+3vz5k1SMBIR+dUpOIiISBKLxfJDThPKz8/n06dPDA4OUlBQ8H+16+3t/aLc4XDgcDjYs2cPmzZtorm5mdLSUpYtW8aTJ09YuHDhqP0tXryYeDyO3+83tiqN5vHjx7hcrj88TxGRn51ejhYRkSQ2m43u7m4ikQivX7/+bn+65nA4qKysxO12c+nSJcLhMIFAgOPHj9Pe3v7Vdk6nk87OTuPzyMgI1dXV+Hw++vv76erqIhAIsGjRIgAOHDjA3bt32b17Nw8ePCAUCnHlyhVqamqM+9uyZQvbt2/n8uXLhMNhfD4fbW1txhiRSISXL1+OGSxERH41Cg4iIpKkrq4Os9lMXl4eM2fOJBqNfre+m5ubcbvd7Nu3j5ycHNavX093d/dXT24C2Lx5M729vTx79gwAs9nM0NAQbrcbh8PBhg0bWLduHUePHgVgyZIl+P1+QqEQBQUF5Ofnc+jQIWbPnm302dTUhMvlYteuXeTm5lJVVZV0XGtrayslJSVkZ2d/t3sXEfm3MyUSicTfPQkREZGxeDwe3r17x6lTp374WLFYDLvdTmtrK6tXr/7h44mI/FvoiYOIiPzj1dfXk52d/Zf8k3N/fz/19fUKDSIiv6MnDiIiIiIikpKeOIiIiIiISEoKDiIiIiIikpKCg4iIiIiIpKTgICIiIiIiKSk4iIiIiIhISgoOIiIiIiKSkoKDiIiIiIikpOAgIiIiIiIpKTiIiIiIiEhK/wGeinkI1N945QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.common import Q_discrete_white_noise\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "from numpy import eye, array, asarray\n",
    "import numpy as np\n",
    "\n",
    "dt = 0.05\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "# make an imperfect starting guess\n",
    "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n",
    "\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]]) * dt\n",
    "\n",
    "range_std = 5. # meters\n",
    "rk.R = np.diag([range_std**2])\n",
    "rk.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
    "rk.Q[2,2] = 0.1\n",
    "rk.P *= 50\n",
    "\n",
    "xs, track = [], []\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    track.append((radar.pos, radar.vel, radar.alt))\n",
    "    \n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    xs.append(rk.x)\n",
    "    rk.predict()\n",
    "\n",
    "xs = asarray(xs)\n",
    "track = asarray(track)\n",
    "time = np.arange(0, len(xs)*dt, dt)\n",
    "ekf_internal.plot_radar(xs, track, time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using SymPy to compute Jacobians\n",
    "\n",
    "Depending on your experience with derivatives you may have found the computation of the Jacobian difficult. Even if you found it easy, a slightly more difficult problem easily leads to very difficult computations.\n",
    "\n",
    "As explained in Appendix A, we can use the SymPy package to compute the Jacobian for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x\\\\x_{vel}\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ x  ⎤\n",
       "⎢    ⎥\n",
       "⎢xᵥₑₗ⎥\n",
       "⎢    ⎥\n",
       "⎣ y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{x}{\\sqrt{x^{2} + y^{2}}} & 0 & \\frac{y}{\\sqrt{x^{2} + y^{2}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡     x                y      ⎤\n",
       "⎢────────────  0  ────────────⎥\n",
       "⎢   _________        _________⎥\n",
       "⎢  ╱  2    2        ╱  2    2 ⎥\n",
       "⎣╲╱  x  + y       ╲╱  x  + y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy\n",
    "from IPython.display import display\n",
    "sympy.init_printing(use_latex='mathjax')\n",
    "\n",
    "x, x_vel, y = sympy.symbols('x, x_vel y')\n",
    "\n",
    "H = sympy.Matrix([sympy.sqrt(x**2 + y**2)])\n",
    "\n",
    "state = sympy.Matrix([x, x_vel, y])\n",
    "J = H.jacobian(state)\n",
    "\n",
    "display(state)\n",
    "display(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This result is the same as the result we computed above, and with much less effort on our part!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Robot Localization\n",
    "\n",
    "It's time to try a real problem. I warn you that this section is difficult. However, most books choose simple, textbook problems with simple answers, and you are left wondering how to solve a real world problem. \n",
    "\n",
    "We will consider the problem of robot localization. We already implemented this in the **Unscented Kalman Filter** chapter, and I recommend you read it now if you haven't already.  In this scenario we have a robot that is moving through a landscape using a sensor to detect landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n",
    "\n",
    "The robot has 4 wheels in the same configuration used by automobiles. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n",
    "\n",
    "The robot has a sensor that measures the range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n",
    "\n",
    "Both the process model and measurement models are nonlinear. The EKF accommodates both, so we provisionally conclude that the EKF is a viable choice for this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robot Motion Model\n",
    "\n",
    "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires a complicated set of differential equations. \n",
    "\n",
    "For lower speed robotic applications a simpler *bicycle model* has been found to perform well. This is a depiction of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.plot_bicycle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the **Unscented Kalman Filter** chapter we derived these equations:\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\beta &= \\frac d w \\tan(\\alpha) \\\\\n",
    "x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $\\theta$ is the robot's heading.\n",
    "\n",
    "You do not need to understand this model in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "For our filter we will maintain the position $x,y$ and orientation $\\theta$ of the robot:\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n",
    "\n",
    "Our control input $\\mathbf u$ is the velocity $v$ and steering angle $\\alpha$:\n",
    "\n",
    "$$\\mathbf u = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the System Model\n",
    "\n",
    "We model our system as a nonlinear motion model plus noise.\n",
    "\n",
    "$$\\bar x = f(x, u) + \\mathcal{N}(0, Q)$$\n",
    "\n",
    "\n",
    "\n",
    "Using the motion model for a robot that we created above, we can expand this to\n",
    "\n",
    "$$\\bar{\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}} = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}$$\n",
    "\n",
    "We find The $\\mathbf F$ by taking the Jacobian of $f(x,u)$.\n",
    "\n",
    "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial x} & \n",
    "\\frac{\\partial f_1}{\\partial y} &\n",
    "\\frac{\\partial f_1}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial f_2}{\\partial x} & \n",
    "\\frac{\\partial f_2}{\\partial y} &\n",
    "\\frac{\\partial f_2}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial f_3}{\\partial x} & \n",
    "\\frac{\\partial f_3}{\\partial y} &\n",
    "\\frac{\\partial f_3}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "When we calculate these we get\n",
    "\n",
    "$$\\mathbf F = \\begin{bmatrix}\n",
    "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n",
    "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n",
    "0 & 0 & 1\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "We can double check our work with SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\cos{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 1 & - \\frac{w \\sin{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\sin{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                        ⎛t⋅v⋅tan(α)    ⎞⎤\n",
       "⎢                   w⋅cos⎜────────── + θ⎟⎥\n",
       "⎢        w⋅cos(θ)        ⎝    w         ⎠⎥\n",
       "⎢1  0  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                        ⎛t⋅v⋅tan(α)    ⎞⎥\n",
       "⎢                   w⋅sin⎜────────── + θ⎟⎥\n",
       "⎢        w⋅sin(θ)        ⎝    w         ⎠⎥\n",
       "⎢0  1  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎣0  0                  1                 ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy.abc import alpha, x, y, v, w, R, theta\n",
    "from sympy import symbols, Matrix\n",
    "sympy.init_printing(use_latex=\"mathjax\", fontsize='16pt')\n",
    "time = symbols('t')\n",
    "d = v*time\n",
    "beta = (d/w)*sympy.tan(alpha)\n",
    "r = w/sympy.tan(alpha)\n",
    "\n",
    "fxu = Matrix([[x-r*sympy.sin(theta) + r*sympy.sin(theta+beta)],\n",
    "              [y+r*sympy.cos(theta)- r*sympy.cos(theta+beta)],\n",
    "              [theta+beta]])\n",
    "F = fxu.jacobian(Matrix([x, y, theta]))\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks a bit complicated. We can use SymPy to substitute terms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - R \\cos{\\left(\\theta \\right)} + R \\cos{\\left(\\beta + \\theta \\right)}\\\\0 & 1 & - R \\sin{\\left(\\theta \\right)} + R \\sin{\\left(\\beta + \\theta \\right)}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0  -R⋅cos(θ) + R⋅cos(β + θ)⎤\n",
       "⎢                              ⎥\n",
       "⎢0  1  -R⋅sin(θ) + R⋅sin(β + θ)⎥\n",
       "⎢                              ⎥\n",
       "⎣0  0             1            ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reduce common expressions\n",
    "B, R = symbols('beta, R')\n",
    "F = F.subs((d/w)*sympy.tan(alpha), B)\n",
    "F.subs(w/sympy.tan(alpha), R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This form  verifies that the computation of the Jacobian is correct.\n",
    "\n",
    "Now we can turn our attention to the noise. Here, the noise is in our control input, so it is in *control space*. In other words, we command a specific velocity and steering angle, but we need to convert that into errors in $x, y, \\theta$. In a real system this might vary depending on velocity, so it will need to be recomputed for every prediction. I will choose this as the noise model; for a real robot you will need to choose a model that accurately depicts the error in your system. \n",
    "\n",
    "$$\\mathbf{M} = \\begin{bmatrix}\\sigma_{vel}^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n",
    "\n",
    "If this was a linear problem we would convert from control space to state space using the by now familiar $\\mathbf{FMF}^\\mathsf T$ form. Since our motion model is nonlinear we do not try to find a closed form solution to this, but instead linearize it with a Jacobian which we will name $\\mathbf{V}$. \n",
    "\n",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial v} & \\frac{\\partial f_1}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_2}{\\partial v} & \\frac{\\partial f_2}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_3}{\\partial v} & \\frac{\\partial f_3}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "These partial derivatives become very difficult to work with. Let's compute them with SymPy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}t \\cos{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\t \\sin{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\\\frac{t}{R} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right)}{w}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅cos(β + θ)   w⋅⎝- tan (α) - 1⎠⋅sin(θ)   w⋅⎝- ta\n",
       "⎢t⋅cos(β + θ)  ────────────────────────── - ──────────────────────── + ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                ⎛   2       ⎞                ⎛     2       ⎞            ⎛    \n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅sin(β + θ)   w⋅⎝- tan (α) - 1⎠⋅cos(θ)   w⋅⎝- ta\n",
       "⎢t⋅sin(β + θ)  ────────────────────────── + ──────────────────────── - ───────\n",
       "⎢                        tan(α)                        2                      \n",
       "⎢                                                   tan (α)                   \n",
       "⎢                                                                             \n",
       "⎢                                                  ⎛   2       ⎞              \n",
       "⎢     t                                          d⋅⎝tan (α) + 1⎠              \n",
       "⎢     ─                                          ───────────────              \n",
       "⎣     R                                                 w                     \n",
       "\n",
       " 2       ⎞           ⎤\n",
       "n (α) - 1⎠⋅sin(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       " 2       ⎞           ⎥\n",
       "n (α) - 1⎠⋅cos(β + θ)⎥\n",
       "─────────────────────⎥\n",
       "      2              ⎥\n",
       "   tan (α)           ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎥\n",
       "                     ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = fxu.jacobian(Matrix([v, alpha]))\n",
    "V = V.subs(sympy.tan(alpha)/w, 1/R) \n",
    "V = V.subs(time*v/R, B)\n",
    "V = V.subs(time*v, 'd')\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This should give you an appreciation of how quickly the EKF become mathematically intractable. \n",
    "\n",
    "This gives us the final form of our prediction equations:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar x} &= \\mathbf x + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar P} &=\\mathbf{FPF}^{\\mathsf T} + \\mathbf{VMV}^{\\mathsf T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "This form of linearization is not the only way to predict $\\mathbf x$. For example, we could use a numerical integration technique such as *Runge Kutta* to compute the movement\n",
    "of the robot. This will be required if the time step is relatively large. Things are not as cut and dried with the EKF as for the Kalman filter. For a real problem you have to carefully model your system with differential equations and then determine the most appropriate way to solve that system. The correct approach depends on the accuracy you require, how nonlinear the equations are, your processor budget, and numerical stability concerns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "The robot's sensor provides a noisy bearing and range measurement to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf T$ into a range and bearing to the landmark. If $\\mathbf p$ \n",
    "is the position of a landmark, the range $r$ is\n",
    "\n",
    "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n",
    "\n",
    "The sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n",
    "\n",
    "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n",
    "\n",
    "\n",
    "Thus our measurement model $h$ is\n",
    "\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf z& = h(\\bar{\\mathbf x}, \\mathbf p) &+ \\mathcal{N}(0, R)\\\\\n",
    "&= \\begin{bmatrix}\n",
    "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n",
    "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n",
    "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n",
    "\\end{aligned}$$\n",
    "\n",
    "This is clearly nonlinear, so we need linearize $h$  at $\\mathbf x$ by taking its Jacobian. We compute that with SymPy below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- p_{x} + x}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & \\frac{- p_{y} + y}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & 0\\\\- \\frac{- p_{y} + y}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & - \\frac{p_{x} - x}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡          -pₓ + x                      -p_y + y             ⎤\n",
       "⎢───────────────────────────  ───────────────────────────  0 ⎥\n",
       "⎢   ________________________     ________________________    ⎥\n",
       "⎢  ╱         2            2     ╱         2            2     ⎥\n",
       "⎢╲╱  (pₓ - x)  + (p_y - y)    ╲╱  (pₓ - x)  + (p_y - y)      ⎥\n",
       "⎢                                                            ⎥\n",
       "⎢       -(-p_y + y)                   -(pₓ - x)              ⎥\n",
       "⎢  ──────────────────────       ──────────────────────     -1⎥\n",
       "⎢          2            2               2            2       ⎥\n",
       "⎣  (pₓ - x)  + (p_y - y)        (pₓ - x)  + (p_y - y)        ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px, py = symbols('p_x, p_y')\n",
    "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n",
    "            [sympy.atan2(py-y, px-x) - theta]])\n",
    "z.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to write that as a Python function. For example we might write:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def H_of(x, landmark_pos):\n",
    "    \"\"\" compute Jacobian of H matrix where h(x) computes \n",
    "    the range and bearing to a landmark for state x \"\"\"\n",
    "\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
    "    dist = sqrt(hyp)\n",
    "\n",
    "    H = array(\n",
    "        [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n",
    "         [ (py - x[1, 0]) / hyp,  -(px - x[0, 0]) / hyp, -1]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need to define a function that converts the system state into a measurement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import atan2\n",
    "\n",
    "def Hx(x, landmark_pos):\n",
    "    \"\"\" takes a state variable and returns the measurement\n",
    "    that would correspond to that state.\n",
    "    \"\"\"\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
    "\n",
    "    Hx = array([[dist],\n",
    "                [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n",
    "    return Hx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Design Measurement Noise\n",
    "\n",
    "It is reasonable to assume that the noise of the range and bearing measurements are independent, hence\n",
    "\n",
    "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "We will use `FilterPy`'s `ExtendedKalmanFilter` class to implement the filter. Its `predict()` method uses the standard linear equations for the process model. Ours is nonlinear, so we will have to override `predict()` with our own implementation.  I'll want to also use this class to simulate the robot, so I'll add a method `move()` that computes the position of the robot which both `predict()` and my simulation can call.\n",
    "\n",
    "The matrices for the prediction step are quite large. While writing this code I made several errors before I finally got it working. I only found my errors by using SymPy's `evalf` function. `evalf` evaluates a SymPy `Matrix` with specific values for the variables. I decided to demonstrate this technique to you, and used `evalf` in the Kalman filter code. You'll need to understand a couple of points.\n",
    "\n",
    "First, `evalf` uses a dictionary to specify the values. For example, if your matrix contains an `x` and `y`, you can write\n",
    "\n",
    "```python\n",
    "    M.evalf(subs={x:3, y:17})\n",
    "```\n",
    "    \n",
    "to evaluate the matrix for `x=3` and `y=17`. \n",
    "\n",
    "Second, `evalf` returns a `sympy.Matrix` object. Use `numpy.array(M).astype(float)` to convert it to a NumPy array. `numpy.array(M)` creates an array of  type `object`, which is not what you want.\n",
    "\n",
    "Here is the code for the EKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter as EKF\n",
    "from numpy import array, sqrt\n",
    "class RobotEKF(EKF):\n",
    "    def __init__(self, dt, wheelbase, std_vel, std_steer):\n",
    "        EKF.__init__(self, 3, 2, 2)\n",
    "        self.dt = dt\n",
    "        self.wheelbase = wheelbase\n",
    "        self.std_vel = std_vel\n",
    "        self.std_steer = std_steer\n",
    "\n",
    "        a, x, y, v, w, theta, time = symbols(\n",
    "            'a, x, y, v, w, theta, t')\n",
    "        d = v*time\n",
    "        beta = (d/w)*sympy.tan(a)\n",
    "        r = w/sympy.tan(a)\n",
    "    \n",
    "        self.fxu = Matrix(\n",
    "            [[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n",
    "             [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n",
    "             [theta+beta]])\n",
    "\n",
    "        self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n",
    "        self.V_j = self.fxu.jacobian(Matrix([v, a]))\n",
    "\n",
    "        # save dictionary and it's variables for later use\n",
    "        self.subs = {x: 0, y: 0, v:0, a:0, \n",
    "                     time:dt, w:wheelbase, theta:0}\n",
    "        self.x_x, self.x_y, = x, y \n",
    "        self.v, self.a, self.theta = v, a, theta\n",
    "\n",
    "    def predict(self, u):\n",
    "        self.x = self.move(self.x, u, self.dt)\n",
    "        self.subs[self.x_x] = self.x[0, 0]\n",
    "        self.subs[self.x_y] = self.x[1, 0]\n",
    "\n",
    "        self.subs[self.theta] = self.x[2, 0]\n",
    "        self.subs[self.v] = u[0]\n",
    "        self.subs[self.a] = u[1]\n",
    "\n",
    "        F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n",
    "        V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n",
    "\n",
    "        # covariance of motion noise in control space\n",
    "        M = array([[self.std_vel**2, 0], \n",
    "                   [0, self.std_steer**2]])\n",
    "\n",
    "        self.P = F @ self.P @ F.T + V @ M @ V.T\n",
    "\n",
    "    def move(self, x, u, dt):\n",
    "        hdg = x[2, 0]\n",
    "        vel = u[0]\n",
    "        steering_angle = u[1]\n",
    "        dist = vel * dt\n",
    "\n",
    "        if abs(steering_angle) > 0.001: # is robot turning?\n",
    "            beta = (dist / self.wheelbase) * tan(steering_angle)\n",
    "            r = self.wheelbase / tan(steering_angle) # radius\n",
    "\n",
    "            dx = np.array([[-r*sin(hdg) + r*sin(hdg + beta)], \n",
    "                           [r*cos(hdg) - r*cos(hdg + beta)], \n",
    "                           [beta]])\n",
    "        else: # moving in straight line\n",
    "            dx = np.array([[dist*cos(hdg)], \n",
    "                           [dist*sin(hdg)], \n",
    "                           [0]])\n",
    "        return x + dx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have another issue to handle. The residual is notionally computed as $y = z - h(x)$ but this will not work because our measurement contains an angle in it. Suppose z has a bearing of $1^\\circ$ and $h(x)$ has a bearing of $359^\\circ$. Naively subtracting them would yield a angular difference of $-358^\\circ$, whereas the correct value is $2^\\circ$. We have to write code to correctly compute the bearing residual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual(a, b):\n",
    "    \"\"\" compute residual (a-b) between measurements containing \n",
    "    [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n",
    "    y = a - b\n",
    "    y[1] = y[1] % (2 * np.pi)    # force in range [0, 2 pi)\n",
    "    if y[1] > np.pi:             # move to [-pi, pi)\n",
    "        y[1] -= 2 * np.pi\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the code runs the simulation and plots the results, and shouldn't need too much comment by now. I create a variable `landmarks` that contains the landmark coordinates. I update the simulated robot position 10 times a second, but run the EKF only once per second. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "from math import sqrt, tan, cos, sin, atan2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dt = 1.0\n",
    "\n",
    "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n",
    "    x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "    d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "    a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
    "    z = np.array([[d + randn()*std_rng],\n",
    "                  [a + randn()*std_brg]])\n",
    "    return z\n",
    "\n",
    "def ekf_update(ekf, z, landmark):\n",
    "    ekf.update(z, HJacobian=H_of, Hx=Hx, \n",
    "               residual=residual,\n",
    "               args=(landmark), hx_args=(landmark))\n",
    "    \n",
    "                \n",
    "def run_localization(landmarks, std_vel, std_steer, \n",
    "                     std_range, std_bearing,\n",
    "                     step=10, ellipse_step=20, ylim=None):\n",
    "    ekf = RobotEKF(dt, wheelbase=0.5, std_vel=std_vel, \n",
    "                   std_steer=std_steer)\n",
    "    ekf.x = array([[2, 6, .3]]).T # x, y, steer angle\n",
    "    ekf.P = np.diag([.1, .1, .1])\n",
    "    ekf.R = np.diag([std_range**2, std_bearing**2])\n",
    "\n",
    "    sim_pos = ekf.x.copy() # simulated position\n",
    "    # steering command (vel, steering angle radians)\n",
    "    u = array([1.1, .01]) \n",
    "\n",
    "    plt.figure()\n",
    "    plt.scatter(landmarks[:, 0], landmarks[:, 1],\n",
    "                marker='s', s=60)\n",
    "    \n",
    "    track = []\n",
    "    for i in range(200):\n",
    "        sim_pos = ekf.move(sim_pos, u, dt/10.) # simulate robot\n",
    "        track.append(sim_pos)\n",
    "\n",
    "        if i % step == 0:\n",
    "            ekf.predict(u=u)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], \n",
    "                     std=6, facecolor='k', alpha=0.3)\n",
    "\n",
    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                z = z_landmark(lmark, sim_pos,\n",
    "                               std_range, std_bearing)\n",
    "                ekf_update(ekf, z, lmark)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2],\n",
    "                    std=6, facecolor='g', alpha=0.8)\n",
    "    track = np.array(track)\n",
    "    plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n",
    "    plt.axis('equal')\n",
    "    plt.title(\"EKF Robot localization\")\n",
    "    if ylim is not None: plt.ylim(*ylim)\n",
    "    plt.show()\n",
    "    return ekf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.017 0.035 0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have plotted the landmarks as solid squares. The path of the robot is drawn with a black line. The covariance ellipses for the predict step are light gray, and the covariances of the update are shown in green. To make them visible at this scale I have set the ellipse boundary at 6$\\sigma$.\n",
    "\n",
    "We can see that there is a lot of uncertainty added by our motion model, and that most of the error in in the direction of motion. We determine that from the shape of the blue ellipses. After a few steps we can see that the filter incorporates the landmark measurements and the errors improve.\n",
    "\n",
    "I used the same initial conditions and landmark locations in the UKF chapter. The UKF achieves much better accuracy in terms of the error ellipse. Both perform roughly as well as far as their estimate for $\\mathbf x$ is concerned. \n",
    "\n",
    "Now let's add another landmark."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.014 0.016 0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "plt.show()\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The uncertainly in the estimates near the end of the track are smaller.  We can see the effect that multiple landmarks have on our uncertainty by only using the first two landmarks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.02  0.046 0.   ]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:2], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate quickly diverges from the robot's path after passing the landmarks. The covariance also grows quickly. Let's see what happens with only one landmark:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.249 0.849 0.004]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:1], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you probably suspected, one landmark produces a very bad result. Conversely, a large number of landmarks allows us to make very accurate estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.006 0.007 0.001]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10,  5], [15, 15], [20,  5], [15, 10], \n",
    "                   [10,14], [23, 14], [25, 20], [10, 20]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1, ylim=(0, 21))\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "I said that this was a real problem, and in some ways it is. I've seen alternative presentations that used robot motion models that led to simpler Jacobians. On the other hand, my model of the movement is also simplistic in several ways. First, it uses a bicycle model. A real car has two sets of tires, and each travels on a different radius. The wheels do not grip the surface perfectly. I also assumed that the robot responds instantaneously to the control input. Sebastian Thrun writes in *Probabilistic Robots* that this simplified model is justified because the filters perform well when used to track real vehicles. The lesson here is that while you have to have a reasonably accurate nonlinear model, it does not need to be perfect to operate well. As a designer you will need to balance the fidelity of your model with the difficulty of the math and the CPU time required to perform the linear algebra. \n",
    "\n",
    "Another way in which this problem was simplistic is that we assumed that we knew the correspondance between the landmarks and measurements. But suppose we are using radar - how would we know that a specific signal return corresponded to a specific building in the local scene? This question hints at SLAM algorithms - simultaneous localization and mapping. SLAM is not the point of this book, so I will not elaborate on this topic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## UKF vs EKF\n",
    "\n",
    "\n",
    "In the last chapter I used the UKF to solve this problem. The difference in implementation should be very clear. Computing the Jacobians for the state and measurement models was not trivial despite a rudimentary motion model. A different problem could result in a Jacobian which is difficult or impossible to derive analytically. In contrast, the UKF only requires you to provide a function that computes the system motion model and another for the measurement model. \n",
    "\n",
    "There are many cases where the Jacobian cannot be found analytically. The details are beyond the scope of this book, but you will have to use numerical methods to compute the Jacobian. That undertaking is not trivial, and you will spend a significant portion of a master's degree at a STEM school learning techniques to handle such situations. Even then you'll likely only be able to solve problems related to your field - an aeronautical engineer learns a lot about Navier Stokes equations, but not much about modelling chemical reaction rates. \n",
    "\n",
    "So, UKFs are easy. Are they accurate? In practice they often perform better than the EKF. You can find plenty of research papers that prove that the UKF outperforms the EKF in various problem domains. It's not hard to understand why this would be true. The EKF works by linearizing the system model and measurement model at a single point, and the UKF uses $2n+1$ points.\n",
    "\n",
    "Let's look at a specific example. Take $f(x) = x^3$ and pass a Gaussian distribution through it. I will compute an accurate answer using a monte carlo simulation. I generate 50,000 points randomly distributed according to the Gaussian, pass each through $f(x)$, then compute the mean and variance of the result. \n",
    "\n",
    "The EKF linearizes the function by taking the derivative to find the slope at the evaluation point $x$. This slope becomes the linear function that we use to transform the Gaussian. Here is a plot of that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.12\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
   ],
   "source": [
    "import kf_book.nonlinear_plots as nonlinear_plots\n",
    "nonlinear_plots.plot_ekf_vs_mc()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The EKF computation is rather inaccurate. In contrast, here is the performance of the UKF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.13\n",
      "UKF    mean=1.30, std=1.08\n"
     ]
    }
   ],
   "source": [
    "nonlinear_plots.plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that the computation of the UKF's mean is accurate to 2 decimal places. The standard deviation is slightly off, but you can also fine tune how the UKF computes the distribution by using the $\\alpha$, $\\beta$, and $\\gamma$ parameters for generating the sigma points. Here I used $\\alpha=0.001$, $\\beta=3$, and $\\gamma=1$. Feel free to modify them to see the result. You should be able to get better results than I did. However, avoid over-tuning the UKF for a specific test. It may perform better for your test case, but worse in general."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
